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Singularly perturbed semilinear elliptic equation with boundary-interior layer interaction

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Abstract

In this paper, we consider the phenomenon of the boundary and interior layer interactions for a class of semilinear elliptic equation. Under some appropriate conditions, we get the existence of the exact solution for the problem and its high order uniformly valid expansion.

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References

  1. Jiang Fu-ru, Some questions on the turning point theory in ordinary differential equations,An Academic Thesis Collection for the Conference of Second National Modern Mathematics and Mechanics, Shanghai, China, (1987).

  2. Howes, F.A., Boundary-interior layer interactions in nonlinear singular perturbation theory,Amer. Math. Soc. Memoirs,203 (1978).

  3. Howes, F.A., Differential inequalities of higher order and the asymptotic solution of nonlinear boundary value problems,SIAM.J. Math. Anul.,13, 1 (1982).

    Article  MathSciNet  Google Scholar 

  4. Chang, K.W. and F.A. Howes, Nonlinear perturbution phenomena: Theory and application,Appl. Math. Sci.,56, Springer-Verlag, New York Inc. (1984).

  5. Howes, F.A., Some singularly perturbed superquadratic boundary value problems whose solutions exhibit boundary and shock layer behavior,Nonlinear Analysis,4 (1980), 683–698.

    Article  MATH  MathSciNet  Google Scholar 

  6. Dejager, E.M., Singular elliptic perturbations of vanishing first-order differential operators,Lecture Notes in Math.,280, Springer-Verlag (1972), 73–86.

    Article  MathSciNet  Google Scholar 

  7. Howes, F.A., Singularly perturbed semilinear elliptic boundary value problems,Partial Differential Equations,4, 1 (1979), 1–39.

    MATH  MathSciNet  Google Scholar 

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Communicated by Lin Zong-chi

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Zhe-yan, Z. Singularly perturbed semilinear elliptic equation with boundary-interior layer interaction. Appl Math Mech 13, 77–90 (1992). https://doi.org/10.1007/BF02450430

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  • DOI: https://doi.org/10.1007/BF02450430

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