TY - JOUR
T1 - Inhomogeneous parabolic equations on unbounded metric measure spaces
AU - Falconer, Kenneth John
AU - Hu, Jiaxin
AU - Sun, Yuhua
PY - 2012/10
Y1 - 2012/10
N2 - We study the inhomogeneous semilinear parabolic equation
ut = Δu + up + f(x),
with source term f independent of time and subject to f(x) ≥ 0 and with u(0, x) = φ(x) ≥ 0, for the very general setting of a metric measure space. By establishing Harnack-type inequalities in time t and some powerful estimates, we give sufficient conditions for non-existence, local existence and global existence of weak solutions, depending on the value of p relative to a critical exponent.
AB - We study the inhomogeneous semilinear parabolic equation
ut = Δu + up + f(x),
with source term f independent of time and subject to f(x) ≥ 0 and with u(0, x) = φ(x) ≥ 0, for the very general setting of a metric measure space. By establishing Harnack-type inequalities in time t and some powerful estimates, we give sufficient conditions for non-existence, local existence and global existence of weak solutions, depending on the value of p relative to a critical exponent.
UR - http://journals.cambridge.org/abstract_S0308210511000539
U2 - 10.1017/S0308210511000539
DO - 10.1017/S0308210511000539
M3 - Article
SN - 0308-2105
VL - 142
SP - 1003
EP - 1025
JO - Proceedings of the Royal Society of Edinburgh, Section A: Mathematics
JF - Proceedings of the Royal Society of Edinburgh, Section A: Mathematics
IS - 5
ER -