JournalszaaVol. 19, No. 1pp. 109–120

Domain Identification for Semilinear Elliptic Equations in the Plane: the Zero Flux Case

  • Dang Duc Trong

    National University, Hochiminh City, Vietnam
  • Dang Dinh Ang

    National University, Hochiminh City, Vietnam
Domain Identification for Semilinear Elliptic Equations in the Plane: the Zero Flux Case cover
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Abstract

We consider the problem of identifying the domain ΩRn\Omega \subset \mathbb R^n of a semilinear elliptic equation subject to given Cauchy data on part of the known outer boundary Γ\Gamma and to the zero flux condition on the unknown inner boundary γ\gamma, where it is assumed that Γ\Gamma is a piecewise C1C^1 curve and that γ\gamma is the boundary of a finite disjoint union of simply connected domains, each bounded by a piecewise C1C^1 Jordan curve. It is shown that, under appropriate smoothness conditions, the domain Ω\Omega is uniquely determined. The problem of existence of solution for given data is not considered since it is usually of lesser importance in view of measurement errors giving data for which no solution exists. Keywords: Domain identification, semilinear elliptic

Cite this article

Dang Duc Trong, Dang Dinh Ang, Domain Identification for Semilinear Elliptic Equations in the Plane: the Zero Flux Case. Z. Anal. Anwend. 19 (2000), no. 1, pp. 109–120

DOI 10.4171/ZAA/941