ON THE WELL-POSEDNESS OF A TRANSMISSION EIGENVALUE PROBLEM

B. Cobani and L. Subashi

  DOI:  https://doi.org/10.37418/amsj.9.11.3

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In the theory of partial differential equations a crucial role plays the well-posedness of a given problem. In this paper we deal with the existence and the unicity of a transmission problem with mixed boundary conditions and the dependence of the solutions from the initial data. First we put the problem in its variational form with the help of Lax-Milgram lemma. Then, using the trace theorem and the fact that our problem is elliptic we prove its existence. Using an important theorem on functional analysis theory \cite{1}, we finally show the desired result on well-posedness.

Keywords: Well-posedness, eigenvalue, PDE.

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