带非局部源和吸收项的p-Laplace方程解的性质

Properties of the Solution to the p-Laplacian Equation with Nonlocal Sources and Absorptions

研究一类带齐次Dirichlet边界条件的p-Laplace方程ut-div(|▽u|p-2▽u)=∫0auqdx-kum,x∈Ω,t>0解的爆破性质。其中p>2,q,m≥1,k>0,Ω是RN(N≥1)上边界光滑的有界区域。在一定条件下,运用比较原理和上下解技巧,得到了正解的整体存在性与有限时刻爆破的结论。

The explosive properties of the solution to the p-Laplacian equationut-div（｜▽u｜p-2▽u）=∫a0uqdx-kum,x∈Ω,t0with homogeneous Dirichlet boundary conditions are studied in a bounded domain ΩRN,where p2,q,m≥1,k0.Under appropriate hypotheses,we obtain that the solution either exists globally or explodes in finite time.