一类具强非线性源的退化抛物方程的边值问题

Singular Solutions of a Quasilinear Convection Diffusion Degenerate Parabolic Equation with Absorption

讨论了一类具有强非线性源的退化抛物方程解的存在性,该类方程是在研究可压流体在均匀、各向同性的刚性多孔介质中的流动情况时得到的.本文运用正则化、标准Moser迭代以及嵌入不等式等方法研究了该方程在何种情况下有非平凡解及非常奇异解的问题.

The quasilinear convection diffusion degenerate parabolic equation with measure initial value was discussed. We got this equation when we study that a compressible uid ows in a homogeneous isotropic rigid porous medium. The purpose of this paper is to discuss the conditions that the equation has no-trivial solutions and very singular solutions. The P. D. E. methods such as regularization, Moser iteration and Imbedding Theorem were used to study this problem.