TY - JOUR
T1 - Global and Nonglobal Solutions for Pseudo-Parabolic Equation with Inhomogeneous Terms
AU - Yang , Chunxiao
AU - Fan , Jieyu
AU - Gao , Miao
JO - Journal of Partial Differential Equations
VL - 3
SP - 295
EP - 308
PY - 2024
DA - 2024/08
SN - 37
DO - http://doi.org/10.4208/jpde.v37.n3.5
UR - https://global-sci.org/intro/article_detail/jpde/23344.html
KW - Pseudo-parabolic equation, critical Fujita exponent, global solutions, blow-up.
AB - <p style="text-align: justify;">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 $σ &gt;0.$ We further generalize the weight function $w(x) ∼ |x|^σ$ for $−2&lt;σ&lt;0,$ and discuss the global and non-global solutions to obtain the critical Fujita
exponent.</p>