Abstract:
In this paper, we examine a one-dimensional reaction-diffusion system with different-scale diffusion coefficients, discontinuous reaction functions, and Neumann boundary conditions. We demonstrate that a singular perturbation in the fast-component equation and reaction discontinuities lead to the formation of contrast structures with internal transition layers. Also, we analyze the existence, uniqueness, and asymptotic stability of stationary solutions. The obtained results provide theoretical justification for numerical methods applicable to such systems and enable prediction of behavior of solutions in domains of sharp gradients, which is crucial for developing efficient computational algorithms.
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