具强非线性源的p-Laplace方程的Cauchy问题中的1<p<2情形

On the Cauchy Problem of Evolution p-Laplacian Equations with Strongly Nonlinear Sources when 1 < p < 2

本文研究了Cauchy问题(1.1),(1.2)的可解性及解的性质,得到了为使问题(1.1),(1.2)存在局部解、初值u0应满足的可积性及增长性的充分和必要条件.此外,还讨论了一些临界情况和解的唯一性问题.

We study the solvability of the Cauchy problem (1.1)-(1.2) for the largest possible class of initial values, for which (1.1)-(1.2) has a local solution. Moreover, we also study the critical case related to the initial value u0, for 1 < p < ∞.