In this paper we show that it is possible to estimate the speed of decay (as $t \rightarrow + \infty$) 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.
On the speed of decay of solutions to some partial differential equations / Porzio, M. M.. - In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. - ISSN 1096-0813. - 528:(2023). [10.1016/j.jmaa.2023.127535]
On the speed of decay of solutions to some partial differential equations
M. M. Porzio
2023
Abstract
In this paper we show that it is possible to estimate the speed of decay (as $t \rightarrow + \infty$) 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.| File | Dimensione | Formato | |
|---|---|---|---|
|
Porzio_On the speed_2023.pdf
solo gestori archivio
Tipologia:
Versione editoriale (versione pubblicata con il layout dell'editore)
Licenza:
Tutti i diritti riservati (All rights reserved)
Dimensione
597.19 kB
Formato
Adobe PDF
|
597.19 kB | Adobe PDF | Contatta l'autore |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
