On the speed of decay of solutions to some partial differential equations

被引：3
|
作者：
Porzio, Maria Michaela [1 ]
机构：
[1] Sapienza Univ Roma, Dipartimento Pianificaz Design Tecnol Architettura, Via Flaminia 70, I-00196 Rome, Italy
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2023年 / 528卷 / 02期
关键词：
Decay estimates; Rate of decay; Ultracontractive bounds; Extinction in finite time; Partial differential equations; Nonlinear parabolic equations; CAUCHY-PROBLEM; PARABOLIC EQUATIONS; INITIAL TRACES; DEGENERATE; EXISTENCE; INEQUALITIES; UNIQUENESS; BEHAVIOR; UNIFORM; BOUNDS;
D O I：
10.1016/j.jmaa.2023.127535
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we show that it is possible to estimate the speed of decay (as t & RARR; +& INFIN;) of a function u(t) simply by proving that it satisfies certain integral inequalities. Moreover, we study the relationship between these integral inequalities and the phenomenon of the extinction in finite time proving that the extinction appears for a suitable choice of the exponents in these inequalities. Finally, we give same easy example of possible applications of these general results to the description of the asymptotic behavior of the solutions to some different evolution problems.& COPY; 2023 Elsevier Inc. All rights reserved.
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