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.
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
.
DOI: 10.1007/s10473-023-0520-x
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