TY - JOUR
T1 - Nonlinear degenerate parabolic equations with time dependent singular coefficients
AU - Ahmetolan, S.
AU - Cavdar, S.
PY - 2011/7
Y1 - 2011/7
N2 - We are concerned with the nonexistence of positive solutions of the nonlinear parabolic partial differential equations in a cylinder Ω × (0, T) with initial condition u(, 0) = u0 ≥ 0 and vanishing on the boundary ∂Ω × (0, T), given by where Ω ∈ Rn (resp. a Carnot Carathéodory metric ball in with smooth boundary and the time dependent singular potential function V(x, t) ∈ L1loc(Ω × (0, T)), 1 < p < N, p - 1 + α + β > 0. We find the best lower bounds for p + β and provide proofs for the nonexistence of positive solutions.
AB - We are concerned with the nonexistence of positive solutions of the nonlinear parabolic partial differential equations in a cylinder Ω × (0, T) with initial condition u(, 0) = u0 ≥ 0 and vanishing on the boundary ∂Ω × (0, T), given by where Ω ∈ Rn (resp. a Carnot Carathéodory metric ball in with smooth boundary and the time dependent singular potential function V(x, t) ∈ L1loc(Ω × (0, T)), 1 < p < N, p - 1 + α + β > 0. We find the best lower bounds for p + β and provide proofs for the nonexistence of positive solutions.
KW - Nonlinear parabolic equations
KW - Positive solutions
UR - http://www.scopus.com/inward/record.url?scp=79958788164&partnerID=8YFLogxK
U2 - 10.1002/mana.200810135
DO - 10.1002/mana.200810135
M3 - Article
AN - SCOPUS:79958788164
SN - 0025-584X
VL - 284
SP - 1219
EP - 1233
JO - Mathematische Nachrichten
JF - Mathematische Nachrichten
IS - 10
ER -