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Volume 38, Issue 3
Global and Non-Global Solutions for Pseudo-Parabolic Equation with Singular Potential

Chunxiao Yang, Xinyu Pan & Yuqing Chen

DOI: 10.4208/jpde.v38.n3.5

J. Part. Diff. Eq., 38 (2025), pp. 324-334.

Published online: 2025-09

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  • Abstract

This paper considers initial boundary value to a pseudo-parabolic equation with singular potential $\frac{u_t}{|x|^s}-\Delta u_t-\Delta u =|u|^{p-2}u$ with $2<p<\frac{2N}{N−2},$ which was studied in [1] by Lian et al. They dealt with the global existence, asymptotic behavior with low initial level $J(u_0)≤d$ and got the blow-up conditions of solutions with low and high initial level. In this paper, we give a new blow-up result which independent of the initial Nehari functional $I(u_0)$, and estimate the lower bound for blow-up time under some conditions. Finally, the precise exponential decay estimate is obtained for global solution with some conditions.

  • Keywords

Pseudo-parabolic equation, singular potential, blow-up, bounds for blow up time, exponential decay.

  • AMS Subject Headings

35K70, 35B44

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JPDE-38-324, author = {Yang , ChunxiaoPan , Xinyu and Chen , Yuqing}, title = {Global and Non-Global Solutions for Pseudo-Parabolic Equation with Singular Potential}, journal = {Journal of Partial Differential Equations}, year = {2025}, volume = {38}, number = {3}, pages = {324--334}, abstract = {

This paper considers initial boundary value to a pseudo-parabolic equation with singular potential $\frac{u_t}{|x|^s}-\Delta u_t-\Delta u =|u|^{p-2}u$ with $2<p<\frac{2N}{N−2},$ which was studied in [1] by Lian et al. They dealt with the global existence, asymptotic behavior with low initial level $J(u_0)≤d$ and got the blow-up conditions of solutions with low and high initial level. In this paper, we give a new blow-up result which independent of the initial Nehari functional $I(u_0)$, and estimate the lower bound for blow-up time under some conditions. Finally, the precise exponential decay estimate is obtained for global solution with some conditions.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v38.n3.5}, url = {http://global-sci.org/intro/article_detail/jpde/24404.html} }
TY - JOUR T1 - Global and Non-Global Solutions for Pseudo-Parabolic Equation with Singular Potential AU - Yang , Chunxiao AU - Pan , Xinyu AU - Chen , Yuqing JO - Journal of Partial Differential Equations VL - 3 SP - 324 EP - 334 PY - 2025 DA - 2025/09 SN - 38 DO - http://doi.org/10.4208/jpde.v38.n3.5 UR - https://global-sci.org/intro/article_detail/jpde/24404.html KW - Pseudo-parabolic equation, singular potential, blow-up, bounds for blow up time, exponential decay. AB -

This paper considers initial boundary value to a pseudo-parabolic equation with singular potential $\frac{u_t}{|x|^s}-\Delta u_t-\Delta u =|u|^{p-2}u$ with $2<p<\frac{2N}{N−2},$ which was studied in [1] by Lian et al. They dealt with the global existence, asymptotic behavior with low initial level $J(u_0)≤d$ and got the blow-up conditions of solutions with low and high initial level. In this paper, we give a new blow-up result which independent of the initial Nehari functional $I(u_0)$, and estimate the lower bound for blow-up time under some conditions. Finally, the precise exponential decay estimate is obtained for global solution with some conditions.

Yang , ChunxiaoPan , Xinyu and Chen , Yuqing. (2025). Global and Non-Global Solutions for Pseudo-Parabolic Equation with Singular Potential. Journal of Partial Differential Equations. 38 (3). 324-334. doi:10.4208/jpde.v38.n3.5
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