Finite time blow up and concentration phenomena for a solution to drift-diffusion equations in higher dimensions

Autor: Takayoshi Ogawa, Takeshi Suguro, Hiroshi Wakui
Rok vydání: 2022
Předmět:
Zdroj: Calculus of Variations and Partial Differential Equations. 62
ISSN: 1432-0835
0944-2669
Popis: We show the finite time blow up of a solution to the Cauchy problem of a drift-diffusion equation of a parabolic-elliptic type in higher space dimensions. If the initial data satisfies a certain condition involving the entropy functional, then the corresponding solution to the equation does not exist globally in time and blows up in a finite time for the scaling critical space. Besides there exists a concentration point such that the solution exhibits the concentration in the critical norm. This type of blow up was observed in the scaling critical two dimensions. The proof is based on the profile decomposition and the Shannon inequality in the weighted space.
Databáze: OpenAIRE
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