1. Local well-posedness and global existence for the biharmonic heat equation with exponential nonlinearity
- Author
-
Majdoub, M., Otsmane, S., and Slim Tayachi
- Subjects
35A01 ,Applied Mathematics ,35B40 ,Mathematics::Analysis of PDEs ,35K30 ,35K91 ,Functional Analysis (math.FA) ,Mathematics - Functional Analysis ,Mathematics - Analysis of PDEs ,46E30 ,35K25 ,FOS: Mathematics ,Analysis ,Analysis of PDEs (math.AP) - Abstract
In this paper we prove local well-posedness in Orlicz spaces for the biharmonic heat equation $\partial_{t} u+ \Delta^2 u=f(u),\;t>0,\;x\in\R^N,$ 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 $u\to 0,$ $m$ integer and $N(m-1)/4\geq 2$, we show that the solution is global. Moreover, we obtain a 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., Comment: More explanations was added and some minor misprints was corrected
- Published
- 2016
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