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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.
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
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[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
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