×

zbMATH — the first resource for mathematics

Time discretization of an abstract problem from linearized equations of a coupled sound and heat flow. (English) Zbl 1450.35015
Summary: Recently, a time discretization of simultaneous abstract evolution equations applied to parabolic-hyperbolic phase-field systems has been studied. This article focuses on a time discretization of an abstract problem that has application to linearized equations of coupled sound and heat flow. As examples, we also study some parabolic-hyperbolic phase-field systems.
MSC:
35A35 Theoretical approximation in context of PDEs
35K90 Abstract parabolic equations
35L90 Abstract hyperbolic equations
47J35 Nonlinear evolution equations
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
PDF BibTeX XML Cite
Full Text: Link
References:
[1] V. Barbu;Nonlinear Semigroups and Differential Equations in Banach spaces, Noordhoff International Publishing, Leyden, 1976. · Zbl 0328.47035
[2] V. Barbu;Nonlinear Differential Equations of Monotone Types in Banach Spaces, Springer, New York, 2010. · Zbl 1197.35002
[3] P. Colli, A. Favini;Time discretization of nonlinear Cauchy problems applying to mixed hyperbolic-parabolic equations, Internat. J. Math. Math. Sci.,19(1996), 481-494. · Zbl 0859.35077
[4] P. Colli, S. Kurima;Time discretization of a nonlinear phase-field system in general domains, Commun. Pure Appl. Anal.,18(2019), 3161-3179.
[5] M. Grasselli, V. Pata;Existence of a universal attractor for a parabolic-hyperbolic phase-field system, Adv. Math. Sci. Appl.,13(2003), 443-459. · Zbl 1057.37068
[6] M. Grasselli, V. Pata;Asymptotic behavior of a parabolic-hyperbolic system, Comm. Pure Appl. Anal.,3(2004), 849-881. · Zbl 1079.35022
[7] M. Grasselli, H. Petzeltov´a, G. Schimperna;Convergence to stationary solutions for a parabolic-hyperbolic phase-field system, Commun. Pure Appl. Anal.,5(2006), 827-838. · Zbl 1134.35017
[8] J. W. Jerome;Approximations of Nonlinear Evolution Systems, Mathematics in Science and Engineering164, Academic Press Inc., Orlando, 1983.
[9] S. Kurima;Time discretization of an initial value problem for a simultaneous abstract evolution equation applying to parabolic-hyperbolic phase-field systems, ESAIM Math. Model. Numer. Anal.,54(2020), 977-1002. · Zbl 1437.65120
[10] A. Matsubara, T. Yokota;Applications of the Hille-Yosida theorem to the linearized equations of coupled sound and heat flow, AIMS Mathematics1(2016), 165-177. · Zbl 1428.35104
[11] J. Simon;Compact sets in the spaceLp(0, T;B), Ann. Mat. Pura Appl., (4)146(1987), 65-96. · Zbl 0629.46031
[12] H. Wu, M. Grasselli, S. Zheng;Convergence to equilibrium for a parabolic-hyperbolic phasefield system with Neumann boundary conditions, Math. Models Methods Appl. Sci.,17 (2007), 125-153. · Zbl 1120.35024
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.