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.
- 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