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Local and global existence of solutions to semilinear parabolic initial value problems. (English) Zbl 0963.35075

The paper deals with local and global existence results for the semilinear initial value problem \[ \partial_t u=\sum_{|\alpha |=m} A_\alpha \partial^\alpha_x u+ F(u,\partial_xu,\ldots,\partial^{m-1}_xu),\quad x\in {\mathbb R}^N,\;t>0,\qquad u(x,0)=\varphi(x),\quad x\in {\mathbb R}^N. \]

MSC:

35K30 Initial value problems for higher-order parabolic equations
35K55 Nonlinear parabolic equations
35B40 Asymptotic behavior of solutions to PDEs
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