POSITIVE CLASSICAL SOLUTIONS OF DIRICHLET PROBLEM FOR THE STEADY RELATIVISTIC HEAT EQUATION*

doi:10.1007/s10473-023-0520-x

Abstract

Abstract: In this paper, for a bounded $C^2$ domain, we prove the existence and uniqueness of positive classical solutions to the Dirichlet problem for the steady relativistic heat equation with a class of restricted positive $C^2$ boundary data. We have a non-existence result, which is the justification for taking into account the restricted boundary data. There is a smooth positive boundary datum that precludes the existence of the positive classical solution.

Key words: Dirichlet problem, steady relativistic heat equation, classical solution

CLC Number:

35K65

Tianjie YANG, Guangwei YUAN. POSITIVE CLASSICAL SOLUTIONS OF DIRICHLET PROBLEM FOR THE STEADY RELATIVISTIC HEAT EQUATION^*[J].Acta mathematica scientia,Series B, 2023, 43(5): 2279-2290.

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References

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POSITIVE CLASSICAL SOLUTIONS OF DIRICHLET PROBLEM FOR THE STEADY RELATIVISTIC HEAT EQUATION^*

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