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Volume 37, Issue 1
Quenching Phenomenon of Solutions for Parabolic Equations with Singular Absorption on Graphs

Liping Zhu, Yaxin Zhou & Lin Huang

DOI: 10.4208/jpde.v37.n1.6

J. Part. Diff. Eq., 37 (2024), pp. 104-120.

Published online: 2024-02

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  • Abstract

In this paper, we study the quenching phenomenon of solutions for parabolic equations with singular absorption under the mixed boundary conditions on graphs. Firstly, we prove the local existence of solutions via Schauder fixed point theorem. Then, under certain conditions we obtain the estimates of quenching time and quenching rate. Finally, numerical experiments are shown to explain the theoretical results.

  • Keywords

Graph, singular absorption, quenching, mixed boundary conditions.

  • AMS Subject Headings

35A01, 35B40, 35K67

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JPDE-37-104, author = {Zhu , LipingZhou , Yaxin and Huang , Lin}, title = {Quenching Phenomenon of Solutions for Parabolic Equations with Singular Absorption on Graphs}, journal = {Journal of Partial Differential Equations}, year = {2024}, volume = {37}, number = {1}, pages = {104--120}, abstract = {

In this paper, we study the quenching phenomenon of solutions for parabolic equations with singular absorption under the mixed boundary conditions on graphs. Firstly, we prove the local existence of solutions via Schauder fixed point theorem. Then, under certain conditions we obtain the estimates of quenching time and quenching rate. Finally, numerical experiments are shown to explain the theoretical results.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v37.n1.6}, url = {http://global-sci.org/intro/article_detail/jpde/22908.html} }
TY - JOUR T1 - Quenching Phenomenon of Solutions for Parabolic Equations with Singular Absorption on Graphs AU - Zhu , Liping AU - Zhou , Yaxin AU - Huang , Lin JO - Journal of Partial Differential Equations VL - 1 SP - 104 EP - 120 PY - 2024 DA - 2024/02 SN - 37 DO - http://doi.org/10.4208/jpde.v37.n1.6 UR - https://global-sci.org/intro/article_detail/jpde/22908.html KW - Graph, singular absorption, quenching, mixed boundary conditions. AB -

In this paper, we study the quenching phenomenon of solutions for parabolic equations with singular absorption under the mixed boundary conditions on graphs. Firstly, we prove the local existence of solutions via Schauder fixed point theorem. Then, under certain conditions we obtain the estimates of quenching time and quenching rate. Finally, numerical experiments are shown to explain the theoretical results.

Zhu , LipingZhou , Yaxin and Huang , Lin. (2024). Quenching Phenomenon of Solutions for Parabolic Equations with Singular Absorption on Graphs. Journal of Partial Differential Equations. 37 (1). 104-120. doi:10.4208/jpde.v37.n1.6
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