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Volume 17, Issue 2
The Existence and the Non-existence of Global Solutions of a Free Boundary Problem

Rong Yin & Wanghui Yu

J. Part. Diff. Eq., 17 (2004), pp. 152-162.

Published online: 2004-05

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  • Abstract
We study a free boundary problem of parabolic equations with a positive parameter τ included in the coefficient of the derivative with respect to the time variable t. This problem arises from some reaction-diffusion system. We prove that, if τ is large enough, the solution exists for 0 < t < +∞ while, if τ is small enough, the solution exists only in finite time.
  • Keywords

Free boundary problem global solution existence non-existence

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@Article{JPDE-17-152, author = {}, title = {The Existence and the Non-existence of Global Solutions of a Free Boundary Problem}, journal = {Journal of Partial Differential Equations}, year = {2004}, volume = {17}, number = {2}, pages = {152--162}, abstract = { We study a free boundary problem of parabolic equations with a positive parameter τ included in the coefficient of the derivative with respect to the time variable t. This problem arises from some reaction-diffusion system. We prove that, if τ is large enough, the solution exists for 0 < t < +∞ while, if τ is small enough, the solution exists only in finite time.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5383.html} }
TY - JOUR T1 - The Existence and the Non-existence of Global Solutions of a Free Boundary Problem JO - Journal of Partial Differential Equations VL - 2 SP - 152 EP - 162 PY - 2004 DA - 2004/05 SN - 17 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5383.html KW - Free boundary problem KW - global solution KW - existence KW - non-existence AB - We study a free boundary problem of parabolic equations with a positive parameter τ included in the coefficient of the derivative with respect to the time variable t. This problem arises from some reaction-diffusion system. We prove that, if τ is large enough, the solution exists for 0 < t < +∞ while, if τ is small enough, the solution exists only in finite time.
Rong Yin & Wanghui Yu . (2019). The Existence and the Non-existence of Global Solutions of a Free Boundary Problem. Journal of Partial Differential Equations. 17 (2). 152-162. doi:
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