Global existence and nonexistence of solutions for Newtonian filtration equation. Issue 8 (11th June 2017)

• Record Type: Journal Article
• Authors: Liu, Changchun; Wang, Huimin
• Is Part Of: Applicable analysis. Volume 96:Issue 8(2017)
• Page Start: 1379
• Page End: 1389
• Publication Date: 2017-06-11
• Subjects: Newtonian filtration equation -- nonexistence -- existence; 35B33 -- 35K55 -- 35K65; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2016.1192137
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : In this paper, we study the initial boundary value problem of Newtonian filtration equation in a cone-like do main, where, , with . Let denote the smallest Dirichlet eigenvalue for the Laplace–Beltrami operator on and let l denote the positive root of . We prove that if, then the problem has no global nonnegative solutions for any nonnegative unless ; if, then the problem has global solutions for some .