Regional, single point, and global blow-up for the fourth-order porous medium type equation with source

Details Regional, single point, and global blow-up for the fourth-order porous medium type equation with source Regional, single point, and global blow-up for the fourth-order porous medium type equation with source

2009-01-27

arxiv.org/abs/0901.4279v1

Mathematics

Analysis of PDEs

39 pages, 28 figures

Scientific paper

Three types of blow-up for a fourth-order degenerate reaction-diffusion equation are studied by a combination of analytic and numerical methods. At the critical values of parameters, there occurs a variational problem with a countable set of solutions obtained by Lysternik--Shnirelman category theory, which then are extended to neighbouring values of parameters by a homotopy-like approach.

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