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arXiv · 0901.4307

Five types of blow-up in a semilinear fourth-order reaction-diffusion equation: an analytic-numerical approach

V. A. Galaktionov
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Abstract

Five types of blow-up patterns that can occur for the 4th-order semilinear parabolic equation of reaction-diffusion type $$ u_t= -Δ^2 u + |u|^{p-1} u \quad {in} \quad \ren \times (0,T), p>1, \quad \lim_{t \to T^-}\sup_{x \in \ren} |u(x,t)|= +\iy, $$ are discussed. For the semilinear heat equation $u_t= Δu+ u^p$, various blow-up patterns were under scrutiny since 1980s, while the case of higher-order diffusion was studied much less, regardless a wide range of its application.

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V. A. Galaktionov. 2009-01-27. Five types of blow-up in a semilinear fourth-order reaction-diffusion equation: an analytic-numerical approach. https://doi.org/10.1088/0951-7715%2F22%2F7%2F012

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