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Volume 36, Issue 4
Blowup of the Solutions for a Reaction-Advection-Diffusion Equation with Free Boundaries

Jian Yang

DOI: 10.4208/jpde.v36.n4.5

J. Part. Diff. Eq., 36 (2023), pp. 394-403.

Published online: 2023-11

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  • Abstract

We investigate a blowup problem of a reaction-advection-diffusion equation with double free boundaries and aim to use the dynamics of such a problem to describe the heat transfer and temperature change of a chemical reaction in advective environment with the free boundary representing the spreading front of the heat. We study the influence of the advection on the blowup properties of the solutions and conclude that large advection is not favorable for blowup. Moreover, we give the decay estimates of solutions and the two free boundaries converge to a finite limit for small initial data.

  • Keywords

Nonlinear reaction-advection-diffusion equation, one-phase Stefan problem, decay, blowup.

  • AMS Subject Headings

35K57, 35R35, 80A22, 35B44

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JPDE-36-394, author = {Yang , Jian}, title = {Blowup of the Solutions for a Reaction-Advection-Diffusion Equation with Free Boundaries}, journal = {Journal of Partial Differential Equations}, year = {2023}, volume = {36}, number = {4}, pages = {394--403}, abstract = {

We investigate a blowup problem of a reaction-advection-diffusion equation with double free boundaries and aim to use the dynamics of such a problem to describe the heat transfer and temperature change of a chemical reaction in advective environment with the free boundary representing the spreading front of the heat. We study the influence of the advection on the blowup properties of the solutions and conclude that large advection is not favorable for blowup. Moreover, we give the decay estimates of solutions and the two free boundaries converge to a finite limit for small initial data.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v36.n4.5}, url = {http://global-sci.org/intro/article_detail/jpde/22136.html} }
TY - JOUR T1 - Blowup of the Solutions for a Reaction-Advection-Diffusion Equation with Free Boundaries AU - Yang , Jian JO - Journal of Partial Differential Equations VL - 4 SP - 394 EP - 403 PY - 2023 DA - 2023/11 SN - 36 DO - http://doi.org/10.4208/jpde.v36.n4.5 UR - https://global-sci.org/intro/article_detail/jpde/22136.html KW - Nonlinear reaction-advection-diffusion equation, one-phase Stefan problem, decay, blowup. AB -

We investigate a blowup problem of a reaction-advection-diffusion equation with double free boundaries and aim to use the dynamics of such a problem to describe the heat transfer and temperature change of a chemical reaction in advective environment with the free boundary representing the spreading front of the heat. We study the influence of the advection on the blowup properties of the solutions and conclude that large advection is not favorable for blowup. Moreover, we give the decay estimates of solutions and the two free boundaries converge to a finite limit for small initial data.

Jian Yang. (2023). Blowup of the Solutions for a Reaction-Advection-Diffusion Equation with Free Boundaries. Journal of Partial Differential Equations. 36 (4). 394-403. doi:10.4208/jpde.v36.n4.5
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