Parabolic equations on general bounded domains are studied. Usingthe refined maximum principle, existence and the semigroup property of solutions are obtained. It is also shown that the solution obtained by PDE's ...Parabolic equations on general bounded domains are studied. Usingthe refined maximum principle, existence and the semigroup property of solutions are obtained. It is also shown that the solution obtained by PDE's method has the Feynmann_Kac representation for any bounded domains.展开更多
基金The first author is supported by the Shandong Provincial Natural Science Foundation (No. ZR2014AP005). The second author is supported by the Shandong Provincial Natural Science Foundation (No. ZR2016AQ10), China Scholarship Council (No. 201606225002) and
基金This work was supported by the National Natural Science Foundation of China ( Grant No. 19631020) Mathematical Center of the Ministry of Education of China, Part of the work was completed while the authors were visiting Department of Mathematics, the
文摘Parabolic equations on general bounded domains are studied. Usingthe refined maximum principle, existence and the semigroup property of solutions are obtained. It is also shown that the solution obtained by PDE's method has the Feynmann_Kac representation for any bounded domains.
