On the initial value problem of the semilinear beam equation with weak damping. I: Smoothing effect

DOI10.1016/J.JMAA.2012.12.015zbMath1284.35293OpenAlexW2094864191MaRDI QIDQ1941350

Shuji Yoshikawa, Hiroshi Takeda

Publication date: 12 March 2013

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2012.12.015

zbMATH Keywords

asymptotic profilefourth order wave equation

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Initial value problems for higher-order hyperbolic equations (35L30) Higher-order semilinear hyperbolic equations (35L76)

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Unconditional small data global well-posedness for nonlinear beam equations with weak damping ⋮ Large time behavior of solutions for a PDE model for compressible elastic curve ⋮ Large time behavior of global solutions of the semilinear damped beam equation with slowly decaying data ⋮ Asymptotic profile of solutions to the semilinear beam equation ⋮ Asymptotic behavior for abstract evolution differential equations of second order ⋮ On the initial value problem of the semilinear beam equation with weak damping. II: Asymptotic profiles ⋮ Higher order asymptotic expansion of solutions to abstract linear hyperbolic equations ⋮ Decay estimates for the Cauchy problem for the damped extensible beam equation ⋮ Singular limits in the Cauchy problem for the damped extensible beam equation

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