发展的p-Laplace方程解的障碍行为

Obstruction Phenomenon of the Solution to the Evolution p-Laplace Equation

研究当p∈(1,2)∪(2,+∞)时发展的p-Laplace方程解的障碍现象,得到了慢速扩散情形(p>2)下解的L∞-障碍现象和快速扩散情形(1<p<2)下解的L1-障碍现象.此外,对于具有源项慢速扩散方程,得到了解的有限传播性质.

We studied the obstruction phenomenon arising from the solution of the evolution p-Laplace equation with p ∈ （1,2） ∪ （2, ＋ ∞ ）. The L^∞ -obstruction phenomenon in the case of p 〉 2 （ slow diffusion） and the Ll-obstruction phenomenon in the case of 1 〈 p 〈 2 （fast diffusion） were proved respectively. For the slow diffusion equation with the source term, we also obtained the finite propagation property of solution.