Translator Disclaimer
July/August 2018 Local well-posedness and global existence for the biharmonic heat equation with exponential nonlinearity
Mohamed Majdoub, Sarah Otsmane, Slim Tayachi
Adv. Differential Equations 23(7/8): 489-522 (July/August 2018).

Abstract

In this paper, we prove local well-posedness in Orlicz spaces for the biharmonic heat equation $\partial_{t} u+ \Delta^2 u=f(u),\; t > 0,\; x \in \mathbb R^N,$ with $f(u)\sim \mbox{e}^{u^2}$ for large $u.$ Under smallness condition on the initial data and for exponential nonlinearity $f$ such that $|f(u)|\sim |u|^m$ as $u\to 0,$ $m\geq 2$, $N(m-1)/4\geq 2$, we show that the solution is global. Moreover, we obtain decay estimates for large time for the nonlinear biharmonic heat equation as well as for the nonlinear heat equation. Our results extend to the nonlinear polyharmonic heat equation.

Citation

Download Citation

Mohamed Majdoub. Sarah Otsmane. Slim Tayachi. "Local well-posedness and global existence for the biharmonic heat equation with exponential nonlinearity." Adv. Differential Equations 23 (7/8) 489 - 522, July/August 2018.

Information

Published: July/August 2018
First available in Project Euclid: 11 May 2018

zbMATH: 06889035
MathSciNet: MR3801829

Subjects:
Primary: 35A01, 35B40, 35K25, 35K30, 35K91, 46E30

Rights: Copyright © 2018 Khayyam Publishing, Inc.

JOURNAL ARTICLE
34 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.23 • No. 7/8 • July/August 2018
Back to Top