In this paper we present a necessary and sufficient condition to guarantee that the zeroextended function of the solution for the heat equation in a smaller cylinder is still the solution of the corresponding extensio...In this paper we present a necessary and sufficient condition to guarantee that the zeroextended function of the solution for the heat equation in a smaller cylinder is still the solution of the corresponding extension problem in a larger cylinder.We prove the results under the frameworks of classical solutions,strong solutions and weak solutions.Moreover,we generalize these results to uniformly parabolic equations of divergence form.展开更多
基金Supported by NSFC(Grant No.12071009)the Fundamental Research Funds for the Central Universities(Grant No.lzujbky-2019-21)。
文摘In this paper we present a necessary and sufficient condition to guarantee that the zeroextended function of the solution for the heat equation in a smaller cylinder is still the solution of the corresponding extension problem in a larger cylinder.We prove the results under the frameworks of classical solutions,strong solutions and weak solutions.Moreover,we generalize these results to uniformly parabolic equations of divergence form.
