TY - JOUR
T1 - ON exact dead-core rates for a semilinear heat equation with strong absorption
AU - Seki, Yukihiro
N1 - Funding Information:
The author was supported by Research Fellowships of the Japan Society for the Promotion of Science for Young Scientists.
PY - 2011/2
Y1 - 2011/2
N2 - We study a semilinear heat equation with strong absorption ut = u - up with 0 < p < 1 in RN. A solution is known to develop dead-core in finite time for a wide class of initial data. We construct specific solutions with exact dead-core rates faster than the one given by the corresponding ODE. They are constructed formally by means of matched asymptotic expansion technique and rigorously by means of topological fixed-point arguments based on a priori estimates. To obtain the a priori estimates, we analyze a certain linearized problem in a new function space $\mathcal{H}'$.
AB - We study a semilinear heat equation with strong absorption ut = u - up with 0 < p < 1 in RN. A solution is known to develop dead-core in finite time for a wide class of initial data. We construct specific solutions with exact dead-core rates faster than the one given by the corresponding ODE. They are constructed formally by means of matched asymptotic expansion technique and rigorously by means of topological fixed-point arguments based on a priori estimates. To obtain the a priori estimates, we analyze a certain linearized problem in a new function space $\mathcal{H}'$.
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U2 - 10.1142/S0219199711004154
DO - 10.1142/S0219199711004154
M3 - Article
AN - SCOPUS:79951891333
VL - 13
SP - 1
EP - 52
JO - Communications in Contemporary Mathematics
JF - Communications in Contemporary Mathematics
SN - 0219-1997
IS - 1
ER -