题目：Asymptotic behavior and blow-up of solutions for infinitely degenerate semilinear parabolic equations with logarithmic nonlinearity

报告人：陈化教授（武汉大学）

摘要：

In this talk, we consider the initial-boundary value problem for infinitely degenerate semilinear parabolic equations with  logarithmic nonlinearity $u_t-/triangle_{X} u=u/log|u|$, where $X=(X_1, X_2, /cdots , X_m)$ is an infinitely degenerate system of vector fields, and $/triangle_{X}:=/sum^{m}_{j=1}X^{2}_{j}$ is an infinitely degenerate elliptic operator.  Using potential well method, we first prove the invariance of some sets and vacuum isolating of solutions. Then, by the Galerkin method and the logarithmic Sobolev inequality, we obtain the global existence and blow-up at $+/infty$ of solutions with low initial energy or critical initial energy, and also we discuss the asymptotic behavior of the solutions.

时间：3月28日（周三）上午 8:30--9:30

地点：首师大新教二楼527教室

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