New life-span results for the nonlinear heat equation

被引：4

作者：

Tayachi, Slim ^{[1
]}

Weissler, Fred B. ^{[2
]}

机构：

[1] Univ Tunis El Manar, Fac Sci Tunis, Dept Math, Lab Equat Der Partielles LR03ES04, Tunis 2092, Tunisia

[2] Univ Sorbonne Paris Nord, CNRS UMR LAGA 7539, 99 Ave Jean Baptiste Clement, F-93430 Villetaneuse, France

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2023年 / 373卷

关键词：

Nonlinear heat equation; Hardy-Henon parabolic equations; Local well-posedness; Blowup; Life-span; SEMILINEAR PARABOLIC EQUATION; LARGE TIME BEHAVIOR; LARGE INITIAL DATA; BLOW-UP; CAUCHY-PROBLEM; CRITICAL EXPONENT; GLOBAL EXISTENCE; WELL-POSEDNESS; ZERO POINTS; DIFFUSION;

D O I：

10.1016/j.jde.2023.07.011

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We obtain new estimates for the existence time of the maximal solutions to the nonlinear heat equation regular, sign-changing, as well as non polynomial decaying initial data are considered. The proofs of the lower-bound estimates of life-span are based on the local construction of solutions. The proofs of the upperbounds exploit a well-known necessary condition for the existence of nonnegative solutions. In addition, we establish new results for life-span using dilation methods and we give new life-span estimates for Hardy & COPY; 2023 Elsevier Inc. All rights reserved.

引用

页码：564 / 625

页数：62

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