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The stability of the solutions of an anisotropic diffusion equation

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Abstract

This paper investigates an anisotropic diffusion equation with degeneracy on the boundary. A new kind of weak solution is introduced, and the existence of the nonnegative solution is proved by the parabolically regularized method. Moreover, if the interaction between the convection and the diffusion is considered, the stability of the solutions can be proved without the boundary value condition.

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Acknowledgements

The paper is supported by Natural Science Foundation of Fujian province (No. 2015J01592) and supported by Science Foundation of Xiamen University of Technology (No. XYK201448), China.

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  1. School of Applied Mathematics, Xiamen University of Technology, Xiamen, 361024, China

    Huashui Zhan

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  1. Huashui Zhan
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Correspondence to Huashui Zhan.

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Zhan, H. The stability of the solutions of an anisotropic diffusion equation. Lett Math Phys 109, 1145–1166 (2019). https://doi.org/10.1007/s11005-018-1135-3

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  • DOI: https://doi.org/10.1007/s11005-018-1135-3

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