Abstract
In this paper, the steady-state temperature distribution of heat diffusion on multi-body is considered. Such problems can be regarded as parallel to the existence part of discrete boundary value problems. The steady-state temperature distribution at least exists a nontrivial case when all heat sources are super-linear or sublinear by studying the equivalence of solutions of the heat diffusion equation, solutions of nonlinear algebra equation, and stability point of a function. If all heat source functions are again added the odd conditions, then such a system has 2 n nontrivial solutions. By this fact, we know that the heat diffusion on multi-body may have 2 n nontrivial steady states when the initial temperature distribution is different. Similar results have not been obtained for partial differential equations.
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