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

Five types of blow-up patterns that can occur for the 4th-order semilinear parabolic equation of reaction-diffusion type $$u_t=-{\mathrm{\Delta }}^{2}u+\mathrm{\mid }u{\mathrm{\mid }}^{p-1}uin\text{ren}\times (0,T),p>1,\underset{t\to T^{-}}{\lim }\underset{x\in \text{ren}}{\sup }\mathrm{\mid }u(x,t)\mathrm{\mid }=+\text{iy},$$ are discussed. For the semilinear heat equation $u_t=\mathrm{\Delta }u+u^p$, 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.