On energy decay-nondecay problems for wave equations with nonlinear dissipative term in \(\mathbb{R}^ N\)

DOI10.2969/jmsj/04730405zbMath0835.35093OpenAlexW2005510487MaRDI QIDQ1898876

Kiyoshi Mochizuki, Takahiro Motai

Publication date: 8 November 1995

Published in: Journal of the Mathematical Society of Japan (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2969/jmsj/04730405

zbMATH Keywords

weighted energy estimate

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Second-order nonlinear hyperbolic equations (35L70) Initial value problems for second-order hyperbolic equations (35L15)

Related Items (13)

Asymptotics for the nonlinear dissipative wave equation ⋮ Existence of global decaying solutions to the exterior problem for the Klein-Gordon equation with a nonlinear localized dissipation and a derivative nonlinearity ⋮ The energy decay and asymptotics for a class of semilinear wave equations in two space dimensions ⋮ Blow up for the wave equation with a nonlinear dissipation of cubic convolution type in \(\mathbb R^N\) ⋮ Energy decay for a nonlinear generalized Klein-Gordon equation in exterior domains with a nonlinear localized dissipative term ⋮ Energy decay for systems of semilinear wave equations with dissipative structure in two space dimensions ⋮ Energy decay rates for solutions of the wave equations with nonlinear damping in exterior domain ⋮ On the energy decay for dissipative nonlinear wave equations in one space dimension ⋮ On existence, uniform decay rates and blow up for solutions of the 2-D wave equation with exponential source ⋮ Energy decay and asymptotic behavior of solutions to the wave equations with linear dissipation ⋮ Asymptotic behaviour of solutions for the wave equation with an effective dissipation around the boundary ⋮ Existence of a global attractor for semilinear dissipative wave equations on \(\mathbb{R}^N\) ⋮ Exponential growth for a fractionally damped wave equation

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