摘要
OnthePropertiesoftheSolutionofaStronglyDegenerateParabolicEquationChengFuxia(DepartmentofAppliedMathematics,TsinghuaUniversit...
For a strongly degenerate parabolic equation, we first use the results of Ph. Blanc[1] to get that the Neumann problem may not have a global classical solution. The reason is that the gradients of some local classical solutions blow up in finite time. And under some conditions, we get the global integral solution by the use of semigroup. Then, we give a sufficient condition under which the Neumann problem has a global classical solution. Finally. we study the asymptotic behaviour of the classical solution and prove that the solution converges to the mean of the initial value.
关键词
强退化抛物型方程
解
半群
比较定理
strongly degenerate parabolic equation
semigroup
comparison theorem