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
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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 -