Abstract
This paper is concerned with a time-periodic reaction-diffusion equation in exterior domains \(\Omega ={\mathbb {R}}^N{\setminus } K\), where K is a compact set in \({\mathbb {R}}^N\) and is called an obstacle. We first prove the existence of the entire solution u(t, x) emanating from a time-periodic planar front \(\phi (t,x_1-ct)\) as \(t\rightarrow -\infty \). Then, under the assumption that the propagation of u(t, x) is complete, we prove that u(t, x) converges to the same time-periodic planar front \(\phi (t,x_1-ct)\) as \(t\rightarrow +\infty \) uniformly in \({\overline{\Omega }}\). Finally, we show some examples of geometrical shapes of K such that the propagation of u(t, x) is complete or incomplete.
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Communicated by Rustum Choksi.
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Li, L. Time-Periodic Planar Fronts Around an Obstacle. J Nonlinear Sci 31, 90 (2021). https://doi.org/10.1007/s00332-021-09753-x
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DOI: https://doi.org/10.1007/s00332-021-09753-x