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## Alikakos, Nicholas D.

Compute Distance To:
 Author ID: alikakos.nicholas-d Published as: Alikakos, Nicholas D.; Alikakos, N. D.; Alikakos, Nicholas; Alikakos, N.
 Documents Indexed: 79 Publications since 1979, including 2 Books
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#### Co-Authors

 11 single-authored 33 Fusco, Giorgio 14 Bates, Peter W. 8 Rostamian, Rouben 7 Chen, Xinfu 4 Karali, Georgia D. 3 Fife, Paul C. 2 Faliagas, A. C. 2 Kowalczyk, Michał 2 Smyrnelis, Panayotis 2 Sourdis, Christos 1 Antonopoulos, Panagiotis 1 Betelú, Santiago I. 1 Bronsard, Lia 1 Cahn, John W. 1 Damialis, Apostolos 1 Dougalis, Vassilios A. 1 Freire, Alexandre 1 Gazoulis, Dimitrios 1 Grant, Christopher P. 1 Katzourakis, Nikolaos I. 1 Matano, Hiroshi 1 McKinney, William R. 1 Phillips, Daniel R. 1 Shaing, Ker-Chung 1 Simpson, Henry C. 1 Stefanopoulos, Vangelis 1 Stratis, Ioannis G. 1 Tanoğlu, Gamze B.
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#### Serials

 9 Journal of Differential Equations 6 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 4 Indiana University Mathematics Journal 3 Archive for Rational Mechanics and Analysis 3 Transactions of the American Mathematical Society 3 Communications in Partial Differential Equations 3 Nonlinear Analysis. Theory, Methods & Applications 2 Communications in Mathematical Physics 2 Israel Journal of Mathematics 2 Bulletin of the Greek Mathematical Society 2 European Journal of Applied Mathematics 2 Linear Algebra and its Applications 2 SIAM Journal on Mathematical Analysis 2 Calculus of Variations and Partial Differential Equations 2 Electronic Journal of Differential Equations (EJDE) 2 Discrete and Continuous Dynamical Systems 1 Journal of Statistical Physics 1 Rocky Mountain Journal of Mathematics 1 Journal of Differential Geometry 1 Mathematische Annalen 1 Proceedings of the American Mathematical Society 1 Quarterly of Applied Mathematics 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Differential and Integral Equations 1 The Journal of Geometric Analysis 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Journal of Dynamics and Differential Equations 1 Resenhas do Instituto do Matemática e Estatística da Universidade de São Paulo 1 Abstract and Applied Analysis 1 Interfaces and Free Boundaries 1 Journal of the European Mathematical Society (JEMS) 1 Discrete and Continuous Dynamical Systems. Series B 1 Acta Mathematica Scientia. Series B. (English Edition) 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 1 Progress in Nonlinear Differential Equations and Their Applications
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#### Fields

 69 Partial differential equations (35-XX) 9 Ordinary differential equations (34-XX) 7 Dynamical systems and ergodic theory (37-XX) 7 Fluid mechanics (76-XX) 5 Calculus of variations and optimal control; optimization (49-XX) 5 Mechanics of deformable solids (74-XX) 5 Statistical mechanics, structure of matter (82-XX) 4 Operator theory (47-XX) 4 Numerical analysis (65-XX) 4 Classical thermodynamics, heat transfer (80-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Differential geometry (53-XX) 3 Global analysis, analysis on manifolds (58-XX) 2 Biology and other natural sciences (92-XX) 1 General and overarching topics; collections (00-XX) 1 Integral equations (45-XX) 1 Mechanics of particles and systems (70-XX) 1 Operations research, mathematical programming (90-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Systems theory; control (93-XX)

#### Citations contained in zbMATH Open

69 Publications have been cited 1,309 times in 963 Documents Cited by Year
$$L^p$$ bounds of solutions of reaction-diffusion equations. Zbl 0421.35009
Alikakos, Nicholas D.
1979
Convergence of the Cahn-Hilliard equation to the Hele-Shaw model. Zbl 0828.35105
Alikakos, Nicholas D.; Bates, Peter W.; Chen, Xinfu
1994
An application of the invariance principle to reaction diffusion equations. Zbl 0386.34046
Alikakos, Nicholas D.
1979
Slow motion for the Cahn-Hilliard equation in one space dimension. Zbl 0753.35042
Alikakos, Nicholas; Bates, Peter W.; Fusco, Giorgio
1991
Periodic traveling waves and locating oscillating patterns in multidimensional domains. Zbl 0929.35067
Alikakos, Nicholas D.; Bates, Peter W.; Chen, Xinfu
1999
Large time behavior of solutions of Neumann boundary value problem for the porous medium equation. Zbl 0598.76100
Alikakos, Nicholas D.; Rostamian, Rouben
1981
On the connection problem for potentials with several global minima. Zbl 1162.65060
Alikakos, N. D.; Fusco, G.
2008
Slow dynamics for the Cahn-Hilliard equation in higher space dimensions: The motion of bubbles. Zbl 0906.35049
Alikakos, Nicholas D.; Fusco, Giorgio
1998
Slow dynamics for the Cahn-Hilliard equation in higher space dimensions. I: Spectral estimates. Zbl 0814.35042
Alikakos, Nicholas D.; Fusco, Giorgio
1994
Motion of a droplet by surface tension along the boundary. Zbl 0994.35052
Alikakos, Nicholas D.; Chen, Xinfu; Fusco, Giorgio
2000
Continuity of the gradient for weak solutions of a degenerate parabolic equation. Zbl 0529.35039
Alikakos, Nicholas D.; Evans, Lawrence C.
1983
Discrete order preserving semigroups and stability for periodic parabolic differential equations. Zbl 0698.35075
Alikakos, Nicholas D.; Hess, Peter; Matano, Hiroshi
1989
The spectrum of the Cahn-Hilliard operator for generic interface in higher space dimensions. Zbl 0798.35123
Alikakos, Nicholas D.; Fusco, Giorgio
1993
Gradient estimates for degenerate diffusion equations. I. Zbl 0465.35051
Alikakos, Nicholas D.; Rostamian, Rouben
1982
Explicit stationary solutions in multiple well dynamics and non-uniqueness of interfacial energy densities. Zbl 1165.35363
Alikakos, Nicholas D.; Betelú, Santiago I.; Chen, Xinfu
2006
On the singular limit in a phase field model of phase transitions. Zbl 0696.35060
Alikakos, Nicholas D.; Bates, Peter W.
1988
Entire solutions to equivariant elliptic systems with variational structure. Zbl 1266.35055
Alikakos, Nicholas D.; Fusco, Giorgio
2011
Some basic facts on the system $$\Delta u - W_{u} (u) = 0$$. Zbl 1210.35069
Alikakos, Nicholas D.
2011
Solutions to the nonautonomous bistable equation with specified Morse index. I: Existence. Zbl 0788.34012
Alikakos, Nicholas D.; Bates, Peter W.; Fusco, Giorgio
1993
Critical spectrum and stability of interfaces for a class of reaction-diffusion equations. Zbl 0879.35074
Alikakos, Nicholas D.; Fusco, Giorgio; Stefanopoulos, Vagelis
1996
Slow motion in the gradient theory of phase transitions via energy and spectrum. Zbl 0910.35146
Alikakos, N. D.; Bronsard, L.; Fusco, G.
1998
On stabilization of discrete monotone dynamical systems. Zbl 0652.47035
Alikakos, Nicholas D.; Hess, Peter
1987
Blow up for a diffusion-advection equation. Zbl 0707.35018
Alikakos, Nicholas D.; Bates, Peter W.; Grant, Christopher P.
1989
On the uniformization of the solutions of the porous medium equation in $$R^ N$$. Zbl 0562.35050
Alikakos, Nicholas D.; Rostamian, Rouben
1984
Regularity and asymptotic behavior for the second order parabolic equation with nonlinear boundary conditions. Zbl 0501.35045
Alikakos, Nicholas D.
1981
The normalized mean curvature flow for a small bubble in a Riemannian manifold. Zbl 1070.53038
Alikakos, Nicholas D.; Freire, Alexandre
2003
On the pointwise behavior of the solutions of the porous medium equation as t approaches zero or infinity. Zbl 0589.35064
Alikakos, Nicholas D.
1985
A variational approach for a class of singular perturbation problems and applications. Zbl 0651.49011
Alikakos, Nicholas D.; Simpson, Henry C.
1987
Critical points of a singular perturbation problem via reduced energy and local linking. Zbl 0942.35078
Alikakos, Nicholas; Kowalczyk, Michał
1999
Ostwald ripening for dilute systems under quasistationary dynamics. Zbl 1082.82005
Alikakos, Nicholas D.; Fusco, Giorgio
2003
A maximum principle for systems with variational structure and an application to standing waves. Zbl 1331.35124
Alikakos, Nicholas D.; Fusco, Giorgio
2015
On the singular limit for a class of problems modelling phase transitions. Zbl 0649.34055
Alikakos, Nicholas D.; Shaing, K. C.
1987
Analysis of a corner layer problem in anisotropic interfaces. Zbl 1235.74011
Alikakos, N. D.; Bates, P. W.; Cahn, J. W.; Fife, P. C.; Fusco, G.; Tanoglu, G. B.
2006
Motion of bubbles towards the boundary for the Cahn-Hilliard equation. Zbl 1065.35136
Alikakos, N. D.; Fusco, G.; Karali, G.
2004
The equations of Ostwald ripening for dilute systems. Zbl 0952.76089
Alikakos, Nicholas D.; Fusco, Giorgio
1999
Finite dimensional dynamics and interfaces intersecting the boundary: Equilibria and quasi-invariant manifold. Zbl 0893.35051
Alikakos, Nicholas D.; Fusco, Giorgio; Kowalszyk, Michał
1996
A new proof for the existence of an equivariant entire solution connecting the minima of the potential for the system $$\Delta u- W_u(u)=0$$. Zbl 1268.35051
Alikakos, Nicholas D.
2012
Remarks on invariance in reaction-diffusion equations. Zbl 0463.35044
Alikakos, Nicholas D.
1981
Gradient estimates for degenerate diffusion equations. II. Zbl 0523.35058
Alikakos, Nicholas D.; Rostamian, Rouben
1982
Ostwald ripening in two dimensions – the rigorous derivation of the equations from the Mullins-Sekerka dynamics. Zbl 1076.35136
Alikakos, Nicholas D.; Fusco, Giorgio; Karali, Georgia
2004
The effect of the geometry of the particle distribution in Ostwald ripening. Zbl 1083.82017
Alikakos, Nicholas D.; Fusco, Giorgio; Karali, Georgia
2003
Stabilization of solutions of the equation (partial d)u / (partial d)t = Delta Phi(u) - beta(u). Zbl 0488.35045
Alikakos, Nicholas D.; Rostamian, Rouben
1982
Heteroclinic travelling waves of gradient diffusion systems. Zbl 1227.35119
Alikakos, Nicholas D.; Katzourakis, Nikolaos I.
2011
Lower bound estimates and separable solutions for homogeneous equations of evolution in Banach space. Zbl 0499.34041
Alikakos, Nicholas D.; Rostamian, Rouben
1982
Asymptotic behavior and rigidity results for symmetric solutions of the elliptic system $$\Delta u = W_u(u)$$. Zbl 1442.35110
Alikakos, Nicholas D.; Fusco, Giorgio
2016
A dynamical systems proof of the Krein-Rutman theorem and an extension of the Perron theorem. Zbl 0727.58043
Alikakos, Nicholas D.; Fusco, Giorgio
1991
On the structure of phase transition maps for three or more coexisting phases. Zbl 1298.35054
Alikakos, Nicholas D.
2013
Stabilization of solutions for a class of degenerate equations in divergence form in one space dimension. Zbl 0671.35006
Alikakos, Nicholas D.; Bates, Peter W.
1988
Equilibrium and dynamics of bubbles for the Cahn-Hilliard equation. Zbl 0938.35565
Alikakos, Nicholas D.; Fusco, Giorgio
1993
Density estimates for vector minimizers and applications. Zbl 1352.35055
Alikakos, Nicholas D.; Fusco, Giorgio
2015
Continuum limits of particles interacting via diffusion. Zbl 1073.35058
Alikakos, Nicholas D.; Fusco, Giorgio; Karali, Georgia
2004
Slow motion manifolds for a class of singular perturbation problems: The linearized equations. Zbl 0808.35058
Alikakos, N. D.; Bates, P. W.; Fusco, G.
1992
Elliptic systems of phase transition type. Zbl 1436.35002
Alikakos, Nicholas D.; Fusco, Giorgio; Smyrnelis, Panayotis
2018
Mullins-Sekerka motion of small droplets on a fixed boundary. Zbl 0984.35013
Alikakos, Nicholas D.; Bates, Peter W.; Chen, Xinfu; Fusco, Giorgio
2000
Singular perturbation problems arising from the anisotropy of crystalline grain boundaries. Zbl 1145.34018
Alikakos, N. D.; Fife, P. C.; Fusco, G.; Sourdis, C.
2007
Analysis of the heteroclinic connection in a singularly perturbed system arising from the study of crystalline grain boundaries. Zbl 1106.35115
Alikakos, N. D.; Fife, P. C.; Fusco, G.; Sourdis, C.
2006
Quantitative maximum principles and strongly coupled gradient-like reaction-diffusion systems. Zbl 0538.35009
Alikakos, Nicholas D.
1983
Estimates for the eigenvalues of the Jordan product of Hermitian matrices. Zbl 0539.15009
Alikakos, N.; Bates, P. W.
1984
On an elliptic system with symmetric potential possessing two global minima. Zbl 1352.35037
Alikakos, Nicholas D.; Fusco, Giorgio
2011
Large time estimates for solutions to the porous medium equation with nonintegrable data via comparison. Zbl 0583.35060
Alikakos, Nicholas D.; Rostamian, Rouben
1985
Stability criteria for multiphase partitioning problems with volume constraints. Zbl 1357.35039
Alikakos, N.; Faliagas, A.
2017
The effect of distribution in space in Ostwald ripening. Zbl 0985.35112
Alikakos, Nicholas D.; Fusco, Giorgio
2001
Some aspects of the dynamics of the Cahn-Hilliard equation. Zbl 0851.35065
Alikakos, N. D.; Fusco, G.
1994
The stress-energy tensor and Pohozaev’s identity for systems. Zbl 1265.49047
Alikakos, N. D.; Faliagas, A. C.
2012
Entire solutions to nonconvex variational elliptic systems in the presence of a finite symmetry group. Zbl 1193.35034
Alikakos, Nicholas D.; Fusco, Giorgio
2009
Classification of initial data for the porous medium equation in $${\mathbb{R}}^ N$$. Zbl 0561.35040
Alikakos, Nicholas D.; Rostamian, Rouben
1984
Remarks on the equilibrium theory for the Cahn-Hilliard equation in one space dimension. Zbl 0722.35082
Alikakos, Nicholas D.; McKinney, William R.
1990
Lyapunov operators and stabilization in strongly order preserving dynamical systems. Zbl 0731.58043
Alikakos, Nicholas D.; Hess, Peter
1991
Existence of lattice solutions to semilinear elliptic systems with periodic potential. Zbl 1239.35043
Alikakos, Nicholas D.; Smyrnelis, Panayotis
2012
Elliptic systems of phase transition type. Zbl 1436.35002
Alikakos, Nicholas D.; Fusco, Giorgio; Smyrnelis, Panayotis
2018
Stability criteria for multiphase partitioning problems with volume constraints. Zbl 1357.35039
Alikakos, N.; Faliagas, A.
2017
Asymptotic behavior and rigidity results for symmetric solutions of the elliptic system $$\Delta u = W_u(u)$$. Zbl 1442.35110
Alikakos, Nicholas D.; Fusco, Giorgio
2016
A maximum principle for systems with variational structure and an application to standing waves. Zbl 1331.35124
Alikakos, Nicholas D.; Fusco, Giorgio
2015
Density estimates for vector minimizers and applications. Zbl 1352.35055
Alikakos, Nicholas D.; Fusco, Giorgio
2015
On the structure of phase transition maps for three or more coexisting phases. Zbl 1298.35054
Alikakos, Nicholas D.
2013
A new proof for the existence of an equivariant entire solution connecting the minima of the potential for the system $$\Delta u- W_u(u)=0$$. Zbl 1268.35051
Alikakos, Nicholas D.
2012
The stress-energy tensor and Pohozaev’s identity for systems. Zbl 1265.49047
Alikakos, N. D.; Faliagas, A. C.
2012
Existence of lattice solutions to semilinear elliptic systems with periodic potential. Zbl 1239.35043
Alikakos, Nicholas D.; Smyrnelis, Panayotis
2012
Entire solutions to equivariant elliptic systems with variational structure. Zbl 1266.35055
Alikakos, Nicholas D.; Fusco, Giorgio
2011
Some basic facts on the system $$\Delta u - W_{u} (u) = 0$$. Zbl 1210.35069
Alikakos, Nicholas D.
2011
Heteroclinic travelling waves of gradient diffusion systems. Zbl 1227.35119
Alikakos, Nicholas D.; Katzourakis, Nikolaos I.
2011
On an elliptic system with symmetric potential possessing two global minima. Zbl 1352.35037
Alikakos, Nicholas D.; Fusco, Giorgio
2011
Entire solutions to nonconvex variational elliptic systems in the presence of a finite symmetry group. Zbl 1193.35034
Alikakos, Nicholas D.; Fusco, Giorgio
2009
On the connection problem for potentials with several global minima. Zbl 1162.65060
Alikakos, N. D.; Fusco, G.
2008
Singular perturbation problems arising from the anisotropy of crystalline grain boundaries. Zbl 1145.34018
Alikakos, N. D.; Fife, P. C.; Fusco, G.; Sourdis, C.
2007
Explicit stationary solutions in multiple well dynamics and non-uniqueness of interfacial energy densities. Zbl 1165.35363
Alikakos, Nicholas D.; Betelú, Santiago I.; Chen, Xinfu
2006
Analysis of a corner layer problem in anisotropic interfaces. Zbl 1235.74011
Alikakos, N. D.; Bates, P. W.; Cahn, J. W.; Fife, P. C.; Fusco, G.; Tanoglu, G. B.
2006
Analysis of the heteroclinic connection in a singularly perturbed system arising from the study of crystalline grain boundaries. Zbl 1106.35115
Alikakos, N. D.; Fife, P. C.; Fusco, G.; Sourdis, C.
2006
Motion of bubbles towards the boundary for the Cahn-Hilliard equation. Zbl 1065.35136
Alikakos, N. D.; Fusco, G.; Karali, G.
2004
Ostwald ripening in two dimensions – the rigorous derivation of the equations from the Mullins-Sekerka dynamics. Zbl 1076.35136
Alikakos, Nicholas D.; Fusco, Giorgio; Karali, Georgia
2004
Continuum limits of particles interacting via diffusion. Zbl 1073.35058
Alikakos, Nicholas D.; Fusco, Giorgio; Karali, Georgia
2004
The normalized mean curvature flow for a small bubble in a Riemannian manifold. Zbl 1070.53038
Alikakos, Nicholas D.; Freire, Alexandre
2003
Ostwald ripening for dilute systems under quasistationary dynamics. Zbl 1082.82005
Alikakos, Nicholas D.; Fusco, Giorgio
2003
The effect of the geometry of the particle distribution in Ostwald ripening. Zbl 1083.82017
Alikakos, Nicholas D.; Fusco, Giorgio; Karali, Georgia
2003
The effect of distribution in space in Ostwald ripening. Zbl 0985.35112
Alikakos, Nicholas D.; Fusco, Giorgio
2001
Motion of a droplet by surface tension along the boundary. Zbl 0994.35052
Alikakos, Nicholas D.; Chen, Xinfu; Fusco, Giorgio
2000
Mullins-Sekerka motion of small droplets on a fixed boundary. Zbl 0984.35013
Alikakos, Nicholas D.; Bates, Peter W.; Chen, Xinfu; Fusco, Giorgio
2000
Periodic traveling waves and locating oscillating patterns in multidimensional domains. Zbl 0929.35067
Alikakos, Nicholas D.; Bates, Peter W.; Chen, Xinfu
1999
Critical points of a singular perturbation problem via reduced energy and local linking. Zbl 0942.35078
Alikakos, Nicholas; Kowalczyk, Michał
1999
The equations of Ostwald ripening for dilute systems. Zbl 0952.76089
Alikakos, Nicholas D.; Fusco, Giorgio
1999
Slow dynamics for the Cahn-Hilliard equation in higher space dimensions: The motion of bubbles. Zbl 0906.35049
Alikakos, Nicholas D.; Fusco, Giorgio
1998
Slow motion in the gradient theory of phase transitions via energy and spectrum. Zbl 0910.35146
Alikakos, N. D.; Bronsard, L.; Fusco, G.
1998
Critical spectrum and stability of interfaces for a class of reaction-diffusion equations. Zbl 0879.35074
Alikakos, Nicholas D.; Fusco, Giorgio; Stefanopoulos, Vagelis
1996
Finite dimensional dynamics and interfaces intersecting the boundary: Equilibria and quasi-invariant manifold. Zbl 0893.35051
Alikakos, Nicholas D.; Fusco, Giorgio; Kowalszyk, Michał
1996
Convergence of the Cahn-Hilliard equation to the Hele-Shaw model. Zbl 0828.35105
Alikakos, Nicholas D.; Bates, Peter W.; Chen, Xinfu
1994
Slow dynamics for the Cahn-Hilliard equation in higher space dimensions. I: Spectral estimates. Zbl 0814.35042
Alikakos, Nicholas D.; Fusco, Giorgio
1994
Some aspects of the dynamics of the Cahn-Hilliard equation. Zbl 0851.35065
Alikakos, N. D.; Fusco, G.
1994
The spectrum of the Cahn-Hilliard operator for generic interface in higher space dimensions. Zbl 0798.35123
Alikakos, Nicholas D.; Fusco, Giorgio
1993
Solutions to the nonautonomous bistable equation with specified Morse index. I: Existence. Zbl 0788.34012
Alikakos, Nicholas D.; Bates, Peter W.; Fusco, Giorgio
1993
Equilibrium and dynamics of bubbles for the Cahn-Hilliard equation. Zbl 0938.35565
Alikakos, Nicholas D.; Fusco, Giorgio
1993
Slow motion manifolds for a class of singular perturbation problems: The linearized equations. Zbl 0808.35058
Alikakos, N. D.; Bates, P. W.; Fusco, G.
1992
Slow motion for the Cahn-Hilliard equation in one space dimension. Zbl 0753.35042
Alikakos, Nicholas; Bates, Peter W.; Fusco, Giorgio
1991
A dynamical systems proof of the Krein-Rutman theorem and an extension of the Perron theorem. Zbl 0727.58043
Alikakos, Nicholas D.; Fusco, Giorgio
1991
Lyapunov operators and stabilization in strongly order preserving dynamical systems. Zbl 0731.58043
Alikakos, Nicholas D.; Hess, Peter
1991
Remarks on the equilibrium theory for the Cahn-Hilliard equation in one space dimension. Zbl 0722.35082
Alikakos, Nicholas D.; McKinney, William R.
1990
Discrete order preserving semigroups and stability for periodic parabolic differential equations. Zbl 0698.35075
Alikakos, Nicholas D.; Hess, Peter; Matano, Hiroshi
1989
Blow up for a diffusion-advection equation. Zbl 0707.35018
Alikakos, Nicholas D.; Bates, Peter W.; Grant, Christopher P.
1989
On the singular limit in a phase field model of phase transitions. Zbl 0696.35060
Alikakos, Nicholas D.; Bates, Peter W.
1988
Stabilization of solutions for a class of degenerate equations in divergence form in one space dimension. Zbl 0671.35006
Alikakos, Nicholas D.; Bates, Peter W.
1988
On stabilization of discrete monotone dynamical systems. Zbl 0652.47035
Alikakos, Nicholas D.; Hess, Peter
1987
A variational approach for a class of singular perturbation problems and applications. Zbl 0651.49011
Alikakos, Nicholas D.; Simpson, Henry C.
1987
On the singular limit for a class of problems modelling phase transitions. Zbl 0649.34055
Alikakos, Nicholas D.; Shaing, K. C.
1987
On the pointwise behavior of the solutions of the porous medium equation as t approaches zero or infinity. Zbl 0589.35064
Alikakos, Nicholas D.
1985
Large time estimates for solutions to the porous medium equation with nonintegrable data via comparison. Zbl 0583.35060
Alikakos, Nicholas D.; Rostamian, Rouben
1985
On the uniformization of the solutions of the porous medium equation in $$R^ N$$. Zbl 0562.35050
Alikakos, Nicholas D.; Rostamian, Rouben
1984
Estimates for the eigenvalues of the Jordan product of Hermitian matrices. Zbl 0539.15009
Alikakos, N.; Bates, P. W.
1984
Classification of initial data for the porous medium equation in $${\mathbb{R}}^ N$$. Zbl 0561.35040
Alikakos, Nicholas D.; Rostamian, Rouben
1984
Continuity of the gradient for weak solutions of a degenerate parabolic equation. Zbl 0529.35039
Alikakos, Nicholas D.; Evans, Lawrence C.
1983
Quantitative maximum principles and strongly coupled gradient-like reaction-diffusion systems. Zbl 0538.35009
Alikakos, Nicholas D.
1983
Gradient estimates for degenerate diffusion equations. I. Zbl 0465.35051
Alikakos, Nicholas D.; Rostamian, Rouben
1982
Gradient estimates for degenerate diffusion equations. II. Zbl 0523.35058
Alikakos, Nicholas D.; Rostamian, Rouben
1982
Stabilization of solutions of the equation (partial d)u / (partial d)t = Delta Phi(u) - beta(u). Zbl 0488.35045
Alikakos, Nicholas D.; Rostamian, Rouben
1982
Lower bound estimates and separable solutions for homogeneous equations of evolution in Banach space. Zbl 0499.34041
Alikakos, Nicholas D.; Rostamian, Rouben
1982
Large time behavior of solutions of Neumann boundary value problem for the porous medium equation. Zbl 0598.76100
Alikakos, Nicholas D.; Rostamian, Rouben
1981
Regularity and asymptotic behavior for the second order parabolic equation with nonlinear boundary conditions. Zbl 0501.35045
Alikakos, Nicholas D.
1981
Remarks on invariance in reaction-diffusion equations. Zbl 0463.35044
Alikakos, Nicholas D.
1981
$$L^p$$ bounds of solutions of reaction-diffusion equations. Zbl 0421.35009
Alikakos, Nicholas D.
1979
An application of the invariance principle to reaction diffusion equations. Zbl 0386.34046
Alikakos, Nicholas D.
1979
all top 5

#### Cited by 1,045 Authors

 27 Alikakos, Nicholas D. 26 Mu, Chunlai 21 Fusco, Giorgio 18 Bates, Peter W. 16 Wei, Juncheng 16 Zheng, Pan 13 Chen, Xinfu 13 Kowalczyk, Michał 12 Karali, Georgia D. 12 Shen, Wenxian 12 Sourdis, Christos 12 Winkler, Michael 11 Zhao, Xiao-Qiang 10 Nakao, Mitsuhiro 10 Shi, Junping 10 Strani, Marta 9 Jin, Hai-Yang 9 Niethammer, Barbara 9 Tao, Youshan 9 Wang, Zhian 8 Hilhorst, Danielle 8 Wang, Jinfeng 8 Wang, Liangchen 8 Zheng, Sining 7 Abels, Helmut 7 Folino, Raffaele 7 Hu, Xuegang 7 Li, Wan-Tong 7 Lin, Ke 7 Novick-Cohen, Amy 7 Peletier, Lambertus Adrianus 7 Sheng, WeiJie 7 Smyrnelis, Panayotis 7 Wang, Yifu 6 Matano, Hiroshi 6 Promislow, Keith Steven 6 Rodríguez-Bernal, Aníbal 6 Rostamian, Rouben 6 Ruan, Shigui 6 Souplet, Philippe 6 Zheng, Jiashan 5 Antonopoulou, Dimitra C. 5 Avrin, Joel D. 5 Del Pino, Manuel A. 5 Fazly, Mostafa 5 Feng, Xiaobing 5 Howard, Peter 5 Li, Dan 5 Li, Yukun 5 Lin, Guo 5 Liu, Ji 5 Montecchiari, Piero 5 Nagai, Toshitaka 5 Negreanu, Mihaela 5 Otto, Felix 5 Rabinowitz, Paul Henry 5 Ward, Michael J. 5 Xiang, Tian 4 Bertsch, Michiel 4 Chen, Caisheng 4 Cosner, Chris 4 Ding, Weiwei 4 Du, Qiang 4 Faliagas, A. C. 4 Fei, Mingwen 4 Jüngel, Ansgar 4 Liu, Chun 4 Lou, Bendong 4 Lowengrub, John Samuel 4 Morgan, Jeff J. 4 Nefedov, Nikolaĭ Nikolaevich 4 Nürnberg, Robert 4 Schimperna, Giulio 4 Shen, Zhongwei 4 Suzuki, Takashi 4 Takáč, Peter 4 Tedeev, Anatoliĭ Fedorovich 4 Vasseur, Alexis F. 4 Wang, Zhi Cheng 4 Wei, Suting 4 Winter, Matthias 4 Wu, YiXiang 4 Yamada, Yoshio 4 Zheng, Songmu 3 Alber, Hans-Dieter 3 Arrieta, José M. 3 Baňas, L’ubomír 3 Bao, Xiongxiong 3 Bartels, Sören 3 Blömker, Dirk 3 Bo, Wei-Jian 3 Bronsard, Lia 3 Caginalp, Gunduz 3 Carrillo de la Plata, José Antonio 3 Dáger, René 3 Dai, Feng 3 Ei, Shin-Ichiro 3 Engler, Hans 3 Feng, Xinlong 3 Feng, Zhaosheng ...and 945 more Authors
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#### Cited in 192 Serials

 119 Journal of Differential Equations 62 Journal of Mathematical Analysis and Applications 32 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 31 Archive for Rational Mechanics and Analysis 31 Nonlinear Analysis. Theory, Methods & Applications 26 Discrete and Continuous Dynamical Systems 20 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 19 ZAMP. Zeitschrift für angewandte Mathematik und Physik 19 Communications in Partial Differential Equations 18 Journal of Dynamics and Differential Equations 18 Calculus of Variations and Partial Differential Equations 18 Nonlinear Analysis. Real World Applications 17 Mathematical Methods in the Applied Sciences 17 Transactions of the American Mathematical Society 16 Proceedings of the American Mathematical Society 16 Discrete and Continuous Dynamical Systems. Series B 15 Applicable Analysis 13 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 12 Physica D 12 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 12 SIAM Journal on Mathematical Analysis 11 Applied Mathematics Letters 10 Computers & Mathematics with Applications 9 Annali di Matematica Pura ed Applicata. Serie Quarta 9 Journal of Functional Analysis 9 Journal de Mathématiques Pures et Appliquées. Neuvième Série 8 SIAM Journal on Applied Mathematics 8 Communications on Pure and Applied Analysis 7 Journal of Computational Physics 7 Journal of Statistical Physics 7 Applied Mathematics and Computation 7 Journal of Computational and Applied Mathematics 7 European Journal of Applied Mathematics 7 Journal of Evolution Equations 7 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 6 Journal of Mathematical Physics 6 Rocky Mountain Journal of Mathematics 6 Journal of Scientific Computing 6 NoDEA. Nonlinear Differential Equations and Applications 6 Abstract and Applied Analysis 6 Mathematical Biosciences and Engineering 5 Nonlinearity 5 SIAM Journal on Numerical Analysis 5 Japan Journal of Industrial and Applied Mathematics 4 Communications in Mathematical Physics 4 Israel Journal of Mathematics 4 Journal of Mathematical Biology 4 Mathematical Notes 4 Mathematics of Computation 4 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 4 Mathematische Nachrichten 4 Numerische Mathematik 4 Siberian Mathematical Journal 4 The Journal of Geometric Analysis 4 Electronic Journal of Differential Equations (EJDE) 4 Comptes Rendus. Mathématique. Académie des Sciences, Paris 4 Multiscale Modeling & Simulation 4 Discrete and Continuous Dynamical Systems. Series S 3 Communications on Pure and Applied Mathematics 3 Journal d’Analyse Mathématique 3 Indiana University Mathematics Journal 3 Mathematische Zeitschrift 3 Studies in Applied Mathematics 3 Chinese Annals of Mathematics. Series B 3 Acta Applicandae Mathematicae 3 Acta Mathematicae Applicatae Sinica. English Series 3 International Journal of Mathematics 3 Journal of Nonlinear Science 3 Journal of Mathematical Sciences (New York) 3 Communications in Nonlinear Science and Numerical Simulation 3 Communications in Contemporary Mathematics 3 Analysis and Applications (Singapore) 3 Mediterranean Journal of Mathematics 3 Kinetic and Related Models 2 Computer Methods in Applied Mechanics and Engineering 2 Journal of Fluid Mechanics 2 Bulletin of Mathematical Biology 2 Advances in Mathematics 2 Applied Mathematics and Optimization 2 Archiv der Mathematik 2 Monatshefte für Mathematik 2 Quarterly of Applied Mathematics 2 Results in Mathematics 2 Tohoku Mathematical Journal. Second Series 2 Zeitschrift für Analysis und ihre Anwendungen 2 Applied Mathematics and Mechanics. (English Edition) 2 Numerical Methods for Partial Differential Equations 2 Asymptotic Analysis 2 Differential Geometry and its Applications 2 Applications of Mathematics 2 Journal of Elasticity 2 Linear Algebra and its Applications 2 Continuum Mechanics and Thermodynamics 2 Physics of Fluids 2 Journal of Mathematical Fluid Mechanics 2 Journal of the European Mathematical Society (JEMS) 2 Advanced Nonlinear Studies 2 Milan Journal of Mathematics 2 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 2 Advances in Difference Equations ...and 92 more Serials
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#### Cited in 38 Fields

 831 Partial differential equations (35-XX) 257 Biology and other natural sciences (92-XX) 98 Fluid mechanics (76-XX) 73 Dynamical systems and ergodic theory (37-XX) 61 Ordinary differential equations (34-XX) 58 Numerical analysis (65-XX) 54 Statistical mechanics, structure of matter (82-XX) 43 Classical thermodynamics, heat transfer (80-XX) 41 Operator theory (47-XX) 35 Calculus of variations and optimal control; optimization (49-XX) 34 Mechanics of deformable solids (74-XX) 25 Differential geometry (53-XX) 22 Global analysis, analysis on manifolds (58-XX) 15 Integral equations (45-XX) 10 Probability theory and stochastic processes (60-XX) 5 Functional analysis (46-XX) 5 Quantum theory (81-XX) 4 Difference and functional equations (39-XX) 3 Mechanics of particles and systems (70-XX) 3 Optics, electromagnetic theory (78-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Potential theory (31-XX) 2 Geophysics (86-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 General and overarching topics; collections (00-XX) 1 Combinatorics (05-XX) 1 Algebraic geometry (14-XX) 1 Real functions (26-XX) 1 Measure and integration (28-XX) 1 Functions of a complex variable (30-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Geometry (51-XX) 1 General topology (54-XX) 1 Algebraic topology (55-XX) 1 Computer science (68-XX) 1 Operations research, mathematical programming (90-XX) 1 Systems theory; control (93-XX)