Smoothing effect and large time behavior of solutions to nonlinear elastic wave equations with viscoelastic term

DOI10.1016/j.na.2022.112826zbMath1486.35101arXiv2109.04628OpenAlexW3200680313MaRDI QIDQ2119420

Hiroshi Takeda, Yoshiyuki Kagei

Publication date: 29 March 2022

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2109.04628

zbMATH Keywords

consistencysmoothing effectasymptotic profiledamping termsnonlinear elastic wave equation

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Asymptotic behavior of solutions to PDEs (35B40) Initial value problems for second-order hyperbolic equations (35L15) Second-order quasilinear hyperbolic equations (35L72)

Related Items (1)

Decay estimates of solutions to nonlinear elastic wave equations with viscoelastic terms in the framework of \(L^p\)-Sobolev spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Hyperbolic partial differential equations
• On the mathematical foundations of elastic stability theory. I
• Global existence and exponential stability of small solutions to nonlinear viscoelasticity
• Besov spaces and applications to difference methods for initial value problems
• On a global in time existence theorem of smooth solutions to a nonlinear wave equation with viscosity
• Pointwise decay estimates for multidimensional Navier-Stokes diffusion waves
• Global existence of nonlinear elastic waves
• Asymptotic profiles of solutions for structural damped wave equations
• Remark on the rate of decay of solutions to linearized compressible Navier-Stokes equations.
• The null condition and global existence of nonlinear elastic waves
• Asymptotic profiles for wave equations with strong damping
• An introduction to continuum mechanics
• Global and almost global existence of small solutions to a dissipative wave equation in 3D with nearly null nonlinear terms
• Local and global smoothing effects for some linear hyperbolic equations with a strong dissipation
• Semilinear structural damped waves
• Classical Fourier Analysis
• Global existence of small solutions to a class of nonlinear evolution equations
• Global solutions of nonlinear hyperbolic equations for small initial data
• Local existence of solution for the initial boundary value problem of fully nonlinear wave equation
• Multi-dimensional diffusion waves for the Navier-Stokes equations of compressible flow
• On the existence of solutions to the equation \(u_{tt}=u_{xxt}+\sigma (u_x)_x\)

This page was built for publication: Smoothing effect and large time behavior of solutions to nonlinear elastic wave equations with viscoelastic term