一类热方程边值问题解的存在唯一性
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摘要
研究一类热方程具狄利克雷边界条件的第一边值问题.利用Poincar伢不等式导出弱解的极值原理,并运用逼近理论和Arzela-Ascoli定理证得了其边值问题解的存在唯一性.
The first boundary value problem for a class of heat equation with dirichlet boundary conditions was dealed. The extremum principle of the weak solution was derived by using Poincare inequality, and the existence and uniqueness of the solution with the boundary value problem was proved by using the approximation theory and arzela-ascoli theorem.
The first boundary value problem for a class of heat equation with dirichlet boundary conditions was dealed. The extremum principle of the weak solution was derived by using Poincare inequality, and the existence and uniqueness of the solution with the boundary value problem was proved by using the approximation theory and arzela-ascoli theorem.
引文
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[5]M. Jamil,R. A. Khan,K. Shah.Existence theory to a class of boundary value problems of hybrid fractional sequential integro-differential equations[J]. Boundary Value Problems,2019(1):1~12.
[6]M.F. Simoes Patrício,Higinio Ramos,Miguel Patrício.Solving initial and boundary value problems of fractional ordinary differential equationsby using collocation and fractional powers[J]. Journal of Computational and Applied Mathematics,2019(3):348~359.
[2]李俊峰.一类具强非线性源的半线性热方程解的性质[J].数学研究,2006,25(4):40~44.
[3]辛巧,王坤.图上带有变指数吸收项的热方程解的熄灭和正性[J].数学的实践与认识,2017(18):201~205.
[4]麻芮,刘海燕,韩菲.抛物型方程极值原理及其简单推广[J].科技风,2018(15):24~25.
[5]M. Jamil,R. A. Khan,K. Shah.Existence theory to a class of boundary value problems of hybrid fractional sequential integro-differential equations[J]. Boundary Value Problems,2019(1):1~12.
[6]M.F. Simoes Patrício,Higinio Ramos,Miguel Patrício.Solving initial and boundary value problems of fractional ordinary differential equationsby using collocation and fractional powers[J]. Journal of Computational and Applied Mathematics,2019(3):348~359.