TY - JOUR

T1 - The degenerate drift-diffusion system with the sobolev critical exponent

AU - Ogawa, Takayoshi

PY - 2011/8

Y1 - 2011/8

N2 - We consider the drift-di usion system of degenerated type. For n ≥ 3, {equation presented} where > 1 and κ = 1. There exists a critical exponent that classifies the global behavior of the weak solution. In particular, we consider the critical case α* = 2n/n+2 = (2*)', where the Talenti function U(x) solving -2*ΔUn-2/n+2 = U in R n classifies the global existence of the weak solution and finite blow-up of the solution.

AB - We consider the drift-di usion system of degenerated type. For n ≥ 3, {equation presented} where > 1 and κ = 1. There exists a critical exponent that classifies the global behavior of the weak solution. In particular, we consider the critical case α* = 2n/n+2 = (2*)', where the Talenti function U(x) solving -2*ΔUn-2/n+2 = U in R n classifies the global existence of the weak solution and finite blow-up of the solution.

KW - Blow-up

KW - Degenerate drift-diffusion

KW - Global weak solution

KW - Sobolev critical

UR - http://www.scopus.com/inward/record.url?scp=84864475274&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84864475274&partnerID=8YFLogxK

U2 - 10.3934/dcdss.2011.4.875

DO - 10.3934/dcdss.2011.4.875

M3 - Article

AN - SCOPUS:84864475274

SN - 1937-1632

VL - 4

SP - 875

EP - 886

JO - Discrete and Continuous Dynamical Systems - Series S

JF - Discrete and Continuous Dynamical Systems - Series S

IS - 4

ER -