×

Generalized solutions of a class of singularly perturbed Robin problems for nonlinear reaction diffusion equations. (English) Zbl 1313.35179

MSC:

35K57 Reaction-diffusion equations
35B25 Singular perturbations in context of PDEs
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] De Jager E M, Jiang F R. The Theory of Singular Perturbation [M]. Amsterdam: North-Holland Publishing Co, 1996.
[2] Barbu L, Morosanu G. Singularly Perturbed Boundary-Value Problems [M]. Basel: Birkhauserm Verlag AG, 2007. · Zbl 1049.34013
[3] Martinez S, Wolanski N. A singular perturbation problem for a quasi-linear operator satisfying the natural condition of Lieberman [J]. SIAM J Math Anal, 2009, 41(1): 318–359. · Zbl 1191.35036 · doi:10.1137/070703740
[4] Kellogg R B, Kopteva N A. Singularly perturbed semilinear reaction-diffusion problem in a polygonal domain [J]. J Differ Equations, 2010, 248(1): 184–208. · Zbl 1184.35022 · doi:10.1016/j.jde.2009.08.020
[5] Tian C R, Zhu P. Existence and asymptotic behavior of solutions for quasilinear parabolic systems [J]. Acta Appl Math, 2012, 121(1): 157–173. · Zbl 1261.35073 · doi:10.1007/s10440-012-9701-7
[6] Skrynnikov Y. Solving initial value problem by matching asymptotic expansions [J]. SIAM J Appl Math, 2012, 72(1): 405–416. · Zbl 1298.35109 · doi:10.1137/100818315
[7] Samusenko P F. Asymptotic integration of degenerate singularly perturbed systems of parabolic partial differential equations [J]. J Math Sci, 2013, 189(5): 834–847. · Zbl 1276.35016 · doi:10.1007/s10958-013-1223-y
[8] Wu Q K, Mo J Q. The nonlinear functional singularly perturbed problems for elliptic equations with boundary perturbation [J]. Acta Anal Functional Appl, 2004, 6(2): 122–127. · Zbl 1134.35353
[9] Mo J Q, Chen X F. Homotopic mapping method of solitary wave solutions for generalized complex Burgers equation [J]. Chin Phys B, 2010, 10(10): 100203.
[10] Mo J Q, Han X L, Chen S L. The singularly perturbed nonlocal reaction diffusion system [J]. Acta Math Sci, 2002, 22B(4): 549–556. · Zbl 1013.35003
[11] Mo J Q, Han X G. A class of singularly perturbed generalized solution for the reaction diffusion problems [J]. J Sys Sci & Math Scis, 2002, 22(4): 447–451. · Zbl 1031.35016
[12] Mo J Q, Lin W T, Wang H. Variational iteration solution of a sea-air oscillator model for the ENSO [J]. Prog Nat Sci, 2007, 17(2): 230–232. · Zbl 1149.86005 · doi:10.1080/10020070612331343252
[13] Mo J Q, Lin W T. A class of nonlinear singularly perturbed problems for reaction diffusion equations with boundary perturbation [J]. Acta Math Appl Sinica English Series, 2006, 22(1): 27–32. · Zbl 1106.35004 · doi:10.1007/s10255-005-0281-4
[14] Mo J Q. A class of singularly perturbed differential-difference reaction diffusion equation [J]. Adv Math, 2009, 38(2): 227–231(Ch).
[15] Mo J Q. Homotopiv mapping solving method for gain fluency of a laser pulse amplifier [J]. Science in China, Ser G, 2009, 52(7): 1007–1070. · doi:10.1007/s11433-009-0146-6
[16] Mo J Q, Lin W T. Asymptotic solution of activator inhibitor systems for nonlinear reaction diffusion equations [J]. J Sys Sci & Complexity, 2008, 20(1): 119–128. · Zbl 1172.93020 · doi:10.1007/s11424-008-9071-4
[17] Mo J Q. Approximate solution of homotopic mapping to solitary wave for generalized nomlinear KdV system [J]. Chin Phys Lett, 2009, 26(1): 010204. · doi:10.1088/0256-307X/26/1/010204
[18] Mo J Q. Singularly perturbed reaction diffusion problem for nonlinear boundary condition with two parameters [J]. Chin Phy, 2010, 19(1): 010203. · Zbl 1240.35022 · doi:10.1088/1674-1056/19/1/010203
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.