具有奇异势和一般非线性的伪抛物方程解的局部存在性和爆破

Local Existence and Blow-Up of Solutions for Pseudo-Parabolic Equation with Singular Potential and General Nonlinearity

In this paper,a semilinear pseudo-parabolic equation with a general nonlin-earity and singular potential is considered.We prove the local existence of solution by Galerkin method and contraction mapping theorem.Moreover,we prove the blow-up of solution and estimate the upper bound of the blow-up time for J(u0)≤0.Finally,we prove the finite time blow-up and estimate the upper bound of blow-up time for J(u0)>0.