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研究了一类p-Laplace发展方程u t=div(Δu p-2Δu)+aurΩ乙uq(x,t)dx在一个有界域Ω奂RN(N>2)解的存在性,其中Δp u=div(Δu p-2Δu),p>1,r,q>0.证明了当r,q≥1时,方程的解唯一存在;而在r<1或者q<1时局部解存在,但唯一性未必成立.
Abstract：This paper studies the existence and uniqueness of solutions for a class of p-Laplace evolution equation u t= div(Δu p- 2 Δu) + aurΩ乙uq(x, t)dx in a bounded domain Ω奂RN with N > 2, where Δp u = div(Δu p- 2 Δu)with p > 1, and r, q > 0. It is shown that the local solution exists and if r, q ≥ 1, the solution is unique and if r, q< 1, the uniqueness doesn't always hold.
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基本信息:
DOI：
中图分类号:O175
引用信息:
[1]张海星,陈玉娟,史金鑫.一类p-Laplace发展方程解的存在性[J],2013,12(03):70-77.
基金信息:
国家自然科学基金项目(11271209);; 江苏省教育厅自然科学面上项目(12KJB110018);; 江苏省2013年出国留学奖学金项目;; 江苏省高等学校大学生实践创新训练计划项目(2012JSSPITP1493)