Quasilinear wave equations and related nonlinear evolution equations

DOI10.1017/S0027763000019553zbMath0472.35052MaRDI QIDQ3925278

Yoshio Yamada

Publication date: 1981

Published in: Nagoya Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

initial value problemthird-order differential equationsquasilinear wave equationsanalytic semi-group theorydecaying estimatessemi-linear evolution equation of parabolic typevanishing viscousity method

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Second-order nonlinear hyperbolic equations (35L70) Wave equation (35L05) Partial differential equations of mathematical physics and other areas of application (35Q99)

Related Items (13)

Differential equations in a Banach space ⋮ Time decay of solutions of semilinear strongly damped generalized wave equations ⋮ Partition of energy in strongly damped generalized wave equations ⋮ Deterministic homogenization of weakly damped nonlinear hyperbolic-parabolic equations ⋮ On weak solutions for hyperbolic differential inclusion with discontinuous nonlinearities ⋮ Periodic homogenization of parabolic nonstandard monotone operators ⋮ On a doubly damped quasilinear wave equation ⋮ On a quasilinear wave equation with nonlinear damping ⋮ Stability for second order abstract evolution equations ⋮ An explicit lower bound for blow up time in a class of nonlinear wave equations with nonlinear damping and source terms ⋮ Periodic solutions to a one-dimensional strongly nonlinear wave equation with strong dissipation ⋮ Finite-dimensional attractors for the quasi-linear strongly-damped wave equation ⋮ Stability results for hyperbolic and parabolic equations

Cites Work

• The total energy decay of solutions for the wave equation with a dissipative term
• Note on certain nonlinear evolution equations of second order
• A class of semi-linear equations of evolution
• A quasilinear hyperbolic and related third-order equations
• On some nonlinear evolution with the strong dissipation
• Global existence and asymptotics of the solutions of the second-order quasilinear hyperbolic equations with the first-order dissipation
• Energy decay of solutions of dissipative wave equations
• On some nonlinear evolution equations with the strong dissipation. II
• Nonstationary flows of viscous and ideal fluids in \(R^3\)
• Sur les problèmes de Cauchy hyperboliques bien posés
• On the Existence and Uniqueness of Solutions of the Equation
• Some nonlinear evolution equations of second order

This page was built for publication: Quasilinear wave equations and related nonlinear evolution equations