Global existence to the initial-boundary value problem for a system of nonlinear diffusion and wave equations

DOI10.1016/j.jde.2017.09.001zbMath1386.35261OpenAlexW2754495789MaRDI QIDQ2410307

Mitsuhiro Nakao

Publication date: 17 October 2017

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2017.09.001

zbMATH Keywords

global existencenonlinear wave equationnonlinear diffusion equationsystem

Mathematics Subject Classification ID

Quasilinear parabolic equations with (p)-Laplacian (35K92) Initial-boundary value problems for PDEs of mixed type (35M13) Second-order semilinear hyperbolic equations (35L71) Mixed-type systems of PDEs (35M30)

Related Items

GLOBAL EXISTENCE TO THE INITIAL-BOUNDARY VALUE PROBLEM FOR A SYSTEM OF NONLINEAR DIFFUSION AND WAVE EQUATIONS II ⋮ Global well posedness for the semilinear edge-degenerate parabolic equations on singular manifolds ⋮ A blow-up result for a Nakao-type weakly coupled system with nonlinearities of derivative-type ⋮ Remarks on global solutions to the initial-boundary value problem for quasilinear degenerate parabolic equations with a nonlinear source term ⋮ Blow up of solutions of systems of nonlinear equations of thermoelasticity ⋮ Smoothing effects of the initial-boundary value problem for logarithmic type quasilinear parabolic equations ⋮ Global existence and nonexistence for a class of finitely degenerate coupled parabolic systems with high initial energy level ⋮ Blow-up of solutions of coupled parabolic systems and hyperbolic equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Global existence to the initial-boundary value problem for a system of semilinear wave equations
• Asymptotic behavior of solutions for the equations of a viscous heat- conductive gas
• On existence, uniform decay rates and blow up for solutions of systems of nonlinear wave equations with damping and source terms
• On global attractor for nonlinear parabolic equations of \(m\)-Laplacian type
• \(L^ p\)-estimates of solutions of some nonlinear degenerate diffusion equations
• Decay of solutions of some nonlinear evolution equations
• Global existence and gradient estimates for the quasilinear parabolic equations of \(m\)-Laplacian type with a nonlinear convection term
• On global solution of nonlinear hyperbolic equations
• On continuity of functions with values in various Banach spaces
• Existence and nonexistence of global solutions for nonlinear parabolic equations
• Large-time behaviour of solutions to hyperbolic–parabolic systems of conservation laws and applications