Year: 2022
Author: Junqiang Han
Journal of Partial Differential Equations, Vol. 35 (2022), Iss. 4 : pp. 307–319
Abstract
The purpose of this paper is to investigate the nonexistence of positive solutions of the following doubly nonlinear degenerate parabolic equations: {∂u∂t=∇k⋅(um−1|∇ku|p−2∇ku)+V(w)um+p−2,in Ω×(0,T),u(w,0)=u0(w)⩾0,in Ω,u(w,t)=0,on ∂Ω×(0,T), where Ω is a Carnot-Carathéodory metric ball in R2n+1 generated by Greiner vector fields, V∈L1loc(Ω), k∈N, m∈R, 1<p<2n+2k and m+p−2>0. The better lower bound p∗ for m+p is found and the nonexistence results are proved for p∗⩽m+p<3.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jpde.v35.n4.1
Journal of Partial Differential Equations, Vol. 35 (2022), Iss. 4 : pp. 307–319
Published online: 2022-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 13
Keywords: Doubly nonlinear degenerate parabolic equations Greiner vector fields positive solutions nonexistence Hardy inequality.