Quenching and blowup problems for reaction diffusion equations
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Doctoral thesis (article-based)
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Date
2004-03-26
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Language
en
Pages
27, [83]
Series
Research reports / Helsinki University of Technology, Institute of Mathematics. A, 466
Abstract
In this thesis we study quenching and blowup problems for reaction diffusion equations with Cauchy-Dirichlet data. We give sufficient conditions for certain reaction terms under which quenching or blowup can occur. Furthermore we show that the set of quenching points is finite for certain nonlinearities. The main results concern the asymptotic behavior of the solution in a neighborhood of a quenching or blowup point. We prove two kinds of asymptotic theorems. First we study quenching or blowup rate results and then give precise asymptotic expressions for solutions in a backward space-time parabola near a quenching point for certain reaction terms.Description
Keywords
reaction-diffusion equation, quenching, quenching set, quenching rate, asymptotic behavior of solutions, refined asymptotics, blow-up, blow-up set, blow-up rate
Other note
Parts
- Salin T., 2003. On quenching with logarithmic singularity. Nonlinear Analysis TMA 52, number 1, pages 261-289.
- Salin T., Quenching-rate estimate for a reaction diffusion equation with weakly singular reaction term. Dynamics of Continuous, Discrete and Impulsive Systems (Series A: Mathematical Analysis), to appear.
- Salin T., 2003. On a refined asymptotic analysis for the quenching problem. Helsinki University of Technology, Institute of Mathematics, Research Report A457.
- Salin T., 2003. The quenching problem for the N-dimensional ball. Helsinki University of Technology, Institute of Mathematics, Research Report A459.