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Solution of contrast structure type for a reaction-diffusion equation with discontinuous reactive term

  • * Corresponding author: Mingkang Ni

    * Corresponding author: Mingkang Ni
The second author is supported by the National Natural Science Foundation of China (No. 11871217) and the Science and Technology Commission of Shanghai Municipality (No. 18dz2271000)
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  • In this paper, we consider the Dirichlet boundary value problem for a singularly perturbed reaction-diffusion equation with discontinuous reactive term. We use the asymptotic analysis to construct the formal asymptotic approximation of the solution with internal and boundary layers. The internal layer is located in the vicinity of a curve of the discontinuous reactive term. By using sufficiently precise lower and upper solutions, we prove the existence of a periodic solution and estimate the accuracy of its asymptotic approximation.

    Mathematics Subject Classification: Primary: 34D15, 34E15; Secondary: 34K13.

    Citation:

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  • Figure 1.  the picture for the zero approximation $ U_{0}(x,t,\epsilon) $ for the solution $ u(x,t,\epsilon) $ of (50)

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