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arXiv · 1711.01499

Large-time behavior of solutions of parabolic equations on the real line with convergent initial data

Antoine Pauthier·Peter Poláčik
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Abstract

We consider the semilinear parabolic equation $u_t=u_{xx}+f(u)$ on the real line, where $f$ is a locally Lipschitz function on $\mathbb{R}.$ We prove that if a solution $u$ of this equation is bounded and its initial value $u(x,0)$ has distinct limits at $x=\pm\infty,$ then the solution is quasiconvergent, that is, all its limit profiles as $t\to\infty$ are steady states.

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Antoine Pauthier, Peter Poláčik. 2020-02-24. Large-time behavior of solutions of parabolic equations on the real line with convergent initial data. https://doi.org/10.1088/1361-6544%2Faaced3

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