TY - JOUR
T1 - Existence of solutions to the slow diffusion equation with a nonlinear source
AU - Sato, Ryuichi
N1 - Funding Information:
This research was partially supported by Grant-in-Aid for Early-Career Scientists JSPS KAKENHI Grant Number 18K13435 . The author would like to thank Professor Kazuhiro Ishige for giving kind and helpful advices. He also thank the referee for his/her careful reading.
Publisher Copyright:
© 2019 Elsevier Inc.
PY - 2020/4/15
Y1 - 2020/4/15
N2 - In this paper we consider the existence of solutions to Cauchy problem for the slow diffusion equation with a source term ∂tu=Δum+up, x∈RN, t>0, u(x,0)=φ(x)≥0, where m≥1 and p>m. Our purpose is to obtain lower estimates of the existence time of solutions in the uniformly local Lebesgue spaces. Furthermore, we obtain the estimate of blow-up time, blow-up rate of solutions and blow-up of critical norm.
AB - In this paper we consider the existence of solutions to Cauchy problem for the slow diffusion equation with a source term ∂tu=Δum+up, x∈RN, t>0, u(x,0)=φ(x)≥0, where m≥1 and p>m. Our purpose is to obtain lower estimates of the existence time of solutions in the uniformly local Lebesgue spaces. Furthermore, we obtain the estimate of blow-up time, blow-up rate of solutions and blow-up of critical norm.
KW - Existence of solutions
KW - Quasilinear parabolic equation
KW - Uniformly Lebesgue spaces
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U2 - 10.1016/j.jmaa.2019.123721
DO - 10.1016/j.jmaa.2019.123721
M3 - Article
AN - SCOPUS:85076027640
VL - 484
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
SN - 0022-247X
IS - 2
M1 - 123721
ER -