1. A reaction–diffusion model for a class of nonlinear parabolic equations with moving boundaries: Existence, uniqueness, exponential decay and simulation.
- Author
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Robalo, Rui J., Almeida, Rui M.P., Coimbra, Maria do Carmo, and Ferreira, Jorge
- Subjects
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MATHEMATICAL models of diffusion , *NONLINEAR analysis , *DEGENERATE parabolic equations , *SIMULATION methods & models , *BOUNDARY value problems , *NUMERICAL analysis , *ALGORITHMS , *FINITE element method - Abstract
The aim of this paper is to establish the existence, uniqueness and asymptotic behaviour of a strong regular solution for a class of nonlinear equations of reaction–diffusion nonlocal type with moving boundaries: u t - a ∫ Ω t u ( x , t ) dx u xx = f ( x , t ) , ( x , t ) ∈ Q t , u ( α ( t ) , t ) = u ( β ( t ) , t ) = 0 , t > 0 , u ( x , 0 ) = u 0 ( x ) , x ∈ Ω 0 = ] α ( 0 ) , β ( 0 ) [ , where Q t is a bounded non-cylindrical domain defined by Q t = ( x , t ) ∈ R 2 : α ( t ) < x < β ( t ) , for all 0 < t < T . Moreover, we study the properties of the solution and implement a numerical algorithm based on the Moving Finite Element Method (MFEM) with polynomial approximations of any degree, to solve this class of problems. Some numerical tests are investigated to evaluate the performance of our Matlab code based on the MFEM and illustrate the exponential decay of the solution. [ABSTRACT FROM AUTHOR]
- Published
- 2014
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