一类退化抛物方程解的性质

The Properties of the Solution to Some Degenerate Parabolic Equation

对一类具有扰动项的退化抛物方程,考虑其解的性质.即证明扰动问题的解的极限(ε→0)是不含扰动项的退化抛物方程的解.本文是先把具扰动项的退化抛物方程正则化,然后证明正则化问题的解的H lder连续性以及满足的两个不等式,由正则化问题解的性质得到原退化抛物方程的解的性质,最后证明ε→0时解的极限性质.

The properties of the solution to some degenerate parabolic equation with shift element are considered in this paper. The limit（ε→0） of the solution to the problem with shift element is proved to be the solution to the degenerate parabolic equation without shift element. Firstly, the degenerate parabolic equation with shift element is regularized. Secondly, the Holder continuous and two inequalities of the solution to the regularized problem are proved, and then the properties of the solution to the original degenerate equation is gained. Lastly,the properties of the limit（ε→0） of the solution is determined.