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Volume 37, Issue 3
Global and Nonglobal Solutions for Pseudo-Parabolic Equation with Inhomogeneous Terms

Chunxiao Yang, Jieyu Fan & Miao Gao

DOI: 10.4208/jpde.v37.n3.5

J. Part. Diff. Eq., 37 (2024), pp. 295-308.

Published online: 2024-08

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  • 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.

  • Keywords

Pseudo-parabolic equation, critical Fujita exponent, global solutions, blow-up.

  • AMS Subject Headings

35K65, 35B33

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{JPDE-37-295, author = {Yang , ChunxiaoFan , Jieyu and Gao , Miao}, title = {Global and Nonglobal Solutions for Pseudo-Parabolic Equation with Inhomogeneous Terms}, journal = {Journal of Partial Differential Equations}, year = {2024}, volume = {37}, number = {3}, pages = {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.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v37.n3.5}, url = {http://global-sci.org/intro/article_detail/jpde/23344.html} }
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 -

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.

Yang , ChunxiaoFan , Jieyu and Gao , Miao. (2024). Global and Nonglobal Solutions for Pseudo-Parabolic Equation with Inhomogeneous Terms. Journal of Partial Differential Equations. 37 (3). 295-308. doi:10.4208/jpde.v37.n3.5
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