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arXiv · 2605.00550

Asymptotic profiles for the Cauchy problem of semilinear beam equation with two variable coefficients in the subcritical case

Mohamed Ali Hamza·Yuta Wakasugi·Shuji Yoshikawa
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Abstract

In this article, we investigate the asymptotic profile of solutions to the Cauchy problem for a nonlinear beam equation with two variable coefficients in the subcritical nonlinear case. In contrast to our previous result [6], in which the asymptotic profile is governed by the linear heat kernel and the nonlinear effect is asymptotically negligible, the asymptotic profile in the present setting is described by a self-similar solution to the associated nonlinear parabolic equation (constructed in Brezis-Peletier-Terman [1]). The proof relies on delicate energy estimates in weighted spaces formulated in parabolic self-similar variables.

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Mohamed Ali Hamza, Yuta Wakasugi, Shuji Yoshikawa. 2026-05-01. Asymptotic profiles for the Cauchy problem of semilinear beam equation with two variable coefficients in the subcritical case. https://arxiv.org/abs/2605.00550

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