Asymptotically self-similar solutions of the damped wave equation

DOI10.1016/j.na.2010.06.047zbMath1204.35064OpenAlexW2001621193MaRDI QIDQ992825

J. Martínez

Publication date: 10 September 2010

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

Full work available at URL: https://doi.org/10.1016/j.na.2010.06.047

zbMATH Keywords

semilinear parabolic equationself-similar variables

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Singular perturbations in context of PDEs (35B25) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Asymptotic expansions of solutions to PDEs (35C20) Self-similar solutions to PDEs (35C06) Second-order semilinear hyperbolic equations (35L71)

Related Items (3)

Asymptotic profiles for a class of perturbed Burgers equations in one space dimension ⋮ The Cauchy problem for the nonlinear damped wave equation with slowly decaying data ⋮ Decay property of solutions to the wave equation with space‐dependent damping, absorbing nonlinearity, and polynomially decaying data

Cites Work

• Large time behavior of the solutions of a semilinear parabolic equation in \(\mathbb R^ n\)
• Semigroups of linear operators and applications to partial differential equations
• A very singular solution of the heat equation with absorption
• Scaling variables and asymptotic expansions in damped wave equations
• A solution of the constant coefficient heat equation on \(\mathbb R\) with exceptional asymptotic behavior: an explicit construction
• ON ASYMPTOTIC “EIGENFUNCTIONS” OF THE CAUCHY PROBLEM FOR A NONLINEAR PARABOLIC EQUATION
• Variational problems related to self-similar solutions of the heat equation
• Large time behavior of solutions of a dissipative semilnear heat equation
• Stable nongaussian diffusive profiles
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