Qian Zhou, Yuanyuan Nie, Xu Zhou, Wei Guo
Abstract:
This article concerns the quenching phenomenon of the solution to the
Dirichlet problem of a semilinear diffusion equation with convection
and reaction. It is shown that there exists a critical length for the
spatial interval in the sense that the solution exists globally in
time if the length of the spatial interval is less than this number
while the solution quenches if the length is greater than this number.
For the solution quenching at a finite time,
we study the location of the quenching points and the blowing up of
the derivative of the solution with respect to the time.
Submitted April 16, 2015. Published August 10, 2015.
Math Subject Classifications: 35K20, 35B40.
Key Words: Quenching; critical length.
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Qian Zhou School of Mathematics Jilin University Changchun 130012, China email: zhouqian@jlu.edu.cn |
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Yuanyuan Nie School of Mathematics Jilin University Changchun 130012, China email: nieyy@jlu.edu.cn |
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Xu Zhou College of Computer Science and Technology Jilin University Changchun 130012, China email: zhouxu0001@163.com |
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Wei Guo School of Mathematics and Statistics Beihua University Jilin 132013, China email: guoweijilin@163.com |
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