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- W4311897112 abstract "In this paper we prove local well-posedness in Orlicz spaces for the biharmonic heat equation $partial_{t} u+ Delta^2 u=f(u),;t>0,;xinR^N,$ 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 $uto 0,$ $m$ integer and $N(m-1)/4geq 2$, 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." @default.
- W4311897112 created "2023-01-02" @default.
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- W4311897112 date "2016-06-23" @default.
- W4311897112 modified "2023-09-23" @default.
- W4311897112 title "Local well-posedness and global existence for the biharmonic heat equation with exponential nonlinearity" @default.
- W4311897112 doi "https://doi.org/10.48550/arxiv.1606.07320" @default.
- W4311897112 hasPublicationYear "2016" @default.
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