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Asymptotics of the Solution to a Stationary Piecewise-Smooth Reaction-Diffusion-Advection Equation

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Abstract

A singularly perturbed boundary value problem for a piecewise-smooth nonlinear stationary equation of reaction-diffusion-advection type is studied. A new class of problems in the case when the discontinuous curve which separates the domain is monotone with respect to the time variable is considered. The existence of a smooth solution with an internal layer appearing in the neighborhood of some point on the discontinuous curve is studied. An efficient algorithm for constructing the point itself and an asymptotic representation of arbitrary-order accuracy to the solution is proposed. For sufficiently small parameter values, the existence theorem is proved by the technique of matching asymptotic expansions. An example is given to show the effectiveness of their method.

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Acknowledgement

The authors would like to express their deepest gratitude to the anonymous reviewers for their careful work, valuable comments and thoughtful suggestions.

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Authors and Affiliations

  1. College of Science, University of Shanghai for Science and Technology, Shanghai, 200093, China

    Qian Yang

  2. School of Mathematical Sciences, East China Normal University, Shanghai, 200062, China

    Mingkang Ni

  3. Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice, Shanghai, 200241, China

    Mingkang Ni

Authors
  1. Qian Yang
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  2. Mingkang Ni
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Correspondence to Mingkang Ni.

Additional information

This work was 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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Yang, Q., Ni, M. Asymptotics of the Solution to a Stationary Piecewise-Smooth Reaction-Diffusion-Advection Equation. Chin. Ann. Math. Ser. B 44, 81–98 (2023). https://doi.org/10.1007/s11401-023-0006-0

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  • DOI: https://doi.org/10.1007/s11401-023-0006-0

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