Abstract
We consider the non-existence of a time global solution to the Cauchy problem of a degenerate drift-diffusion system with a fast-diffusion exponent. We show that the solution for fast-diffusion cases with the diffusion exponent n/n+2 < α < 1 blows up in a finite time if the initial data satisfy certain conditions involving the free energy. We also show the finite-time blow-up for the radially symmetric case without a finite moment condition.
Original language | English |
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Pages (from-to) | 2073-2093 |
Number of pages | 21 |
Journal | Nonlinearity |
Volume | 32 |
Issue number | 6 |
DOIs | |
Publication status | Published - 2019 May 8 |
Keywords
- degenerate drift-diffusion system, finite-time blow-up, Shannon's inequality, existence of weak solution, free energy, virial law
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)
- Applied Mathematics