Non-existence of nonnegative separate variable solutions to a porous medium equation with spatially dependent nonlinear source

被引：4

作者：

Iagar, Razvan Gabriel ^{[1
]}

Laurencot, Philippe ^{[2
]}

机构：

[1] Univ Rey Juan Carlos, Dept Matemat Aplicada Ciencia Ingn Mat & Tecnol El, Mostoles 28933, Madrid, Spain

[2] Univ Paul Sabatier, Inst Math Toulouse, CNRS UMR 5219, F-31062 Toulouse 9, France

来源：

BULLETIN DES SCIENCES MATHEMATIQUES | 2022年 / 179卷

关键词：

Porous medium equation; Weighted source; Backward self -similar solutions; Pohozaev identity; BLOW-UP;

D O I：

10.1016/j.bulsci.2022.103167

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The non-existence of nonnegative finite energy solutions to V 1/m(x) -& UDelta;V (x) - |x|& USigma;V(x) + m- 1 = 0, x & ISIN; RN, with m > 1, & USigma; > 0, and N > 1, is proven for & USigma; sufficiently large. More precisely, in dimension N > 4, the optimal lower bound on & USigma; for non-existence is identified, namely & USigma; > & USigma;c := 2(m- 1)(N- 1) , 3m + 1 while, in dimensions N & ISIN; {1, 2, 3}, the lower bound derived on & USigma; improves previous ones already established in the literature. A by-product of this result is the non-existence of nonnegative compactly supported separate variable solutions to a porous medium equation with spatially dependent superlinear source.(C) 2022 Elsevier Masson SAS. All rights reserved.

引用

页数：13

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