Abstract
In this article, we study the pointwise estimates of solutions to the nonlinear viscous wave equation in even dimensions (n ≥ 4). We use the Green’s function method. Our approach is on the basis of the detailed analysis of the Green’s function of the linearized system. We show that the decay rates of the solution for the same problem are different in even dimensions and odd dimensions. It is shown that the solution exhibits a generalized Huygens principle.
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The author would give thanks to Professor Weike Wang for helpful discussions.
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Supported by Binzhou University (BZXYL1402).
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Li, N. Pointwise estimates of solutions for the nonlinear viscous wave equation in even dimensions. Acta Math Sci 40, 1001–1019 (2020). https://doi.org/10.1007/s10473-020-0409-x
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DOI: https://doi.org/10.1007/s10473-020-0409-x