Year: 2024
Author: Chunxiao Yang, Jieyu Fan, Miao Gao
Journal of Partial Differential Equations, Vol. 37 (2024), Iss. 3 : pp. 295–308
Abstract
This paper considers the Cauchy problem of pseudo-parabolic equation with inhomogeneous terms $u_t = ∆u+k∆u_t+w(x)u^p (x,t).$ In [1], Li et al. gave the critical Fujita exponent, second critical exponent and the life span for blow-up solutions under $w(x) = |x|^σ$ with $σ >0.$ We further generalize the weight function $w(x) ∼ |x|^σ$ for $−2<σ<0,$ and discuss the global and non-global solutions to obtain the critical Fujita exponent.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jpde.v37.n3.5
Journal of Partial Differential Equations, Vol. 37 (2024), Iss. 3 : pp. 295–308
Published online: 2024-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 14
Keywords: Pseudo-parabolic equation critical Fujita exponent global solutions blow-up.