Mixed problems with parameter


Тип публикации: статья из журнала

Год издания: 2005

Аннотация: Let X be a smooth n-dimensional manifold and D be an open connected set in X with smooth boundary OD. Perturbing the Cauchy problem for an elliptic system Au = f in D with data on a closed set Gamma subset of partial derivativeD, we obtain a family of mixed problems depending on a small parameter epsilon > 0. Although the mixed proПоказать полностьюblems are subjected to a noncoercive boundary condition on partial derivativeD\F in general, each of them is uniquely solvable in an appropriate Hilbert space D-T and the corresponding family {u(epsilon)} of solutions approximates the solution of the Cauchy problem in D-T whenever the solution exists. We also prove that the existence of a solution to the Cauchy problem in D-T is equivalent to the boundedness of the family {u(epsilon)}. We thus derive a solvability condition for the Cauchy problem and an effective method of constructing the solution. Examples for Dirac operators in the Euclidean space R-n are treated. In this case, we obtain a family of mixed boundary problems for the Helmholtz equation.

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Журнал: Russian Journal of Mathematical Physics

Выпуск журнала: Vol. 12, Is. 1

Номера страниц: 97-119

ISSN журнала: 10619208

Место издания: New York

Издатель: Maik Nauka/Interperiodica/Springer


  • Shlapunov A. (Krasnoyarsk State University)
  • Tarkhanov N. (Universitat Potsdam,Institut fur Mathematik)

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