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arXiv · 2302.09314

Heat equation with singular thermal conductivity

Michael Ruzhansky·Mohammed Elamine Sebih·Niyaz Tokmagambetov
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Abstract

In this paper, we study the heat equation with an irregular spatially dependent thermal conductivity coefficient. We prove that it has a solution in an appropriate very weak sense. Moreover, the uniqueness result and consistency with the classical solution if the latter exists are shown. Indeed, we allow the coefficient to be a distribution with a toy example of a Delta-function.

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Michael Ruzhansky, Mohammed Elamine Sebih, Niyaz Tokmagambetov. 2023-02-18. Heat equation with singular thermal conductivity. https://arxiv.org/abs/2302.09314

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