【摘要】 本文研究一类带奇异势项的半线性抛物方程解的初边值问题.首先通过Galerkin方法结合势井理论,利用Hardy-Sobolev不等式克服奇异非线性项估计带来的困难,证明了解的全局存在性;其次构造辅助泛函,借助微分不等式技巧,证明了负初始能量条件下解在有限时间爆破,并获得了爆破时间上界;最后运用凸方法,证明了低初始能量条件下解在有限时间爆破,并获得了爆破时间上界.更多还原

【Abstract】 In this paper, we study the initial boundary value problem for a class of solutions of semilinear parabolic equations with singular potential. Firstly, the Hardy-Sobolev inequality is employed to solve the difficulties caused by nonlinear estimation and to prove the global existence of the solution by combining Galerkin method with potential well theory. Secondly, under negative initial energy conditions,the blows up in finite time of the solution and an upper bound on the blow-up time proved by constructing auxiliary functions and differential inequality technique. Finally, under low initial energy conditions, the blows up in finite time of the solution and an upper bound on the blow-up time obtained by the convex method.更多还原