Department of Differential Equations
Department of Fundamental Mathematics
Institute of Mathematics and Mathematical Modeling
125 Pushkin str., 050010 Almaty, Kazakhistan
email: torebek@math.kz
Berikbol T. Torebek
Abstract:
In this article we consider the Robin-Cauchy problem for multidimensional
elliptic equations in a cylindrical domain. The method of spectral
expansion in eigenfunctions of the Robin-Cauchy problem for equations
with deviating argument establishes a criterion of the strong solvability
of the considered Robin-Cauchy problem. It is shown that the ill-posedness
of the Robin-Cauchy problem is equivalent to the existence of an isolated
point of the continuous spectrum for a self-adjoint operator with the
deviating argument.
Submitted
Submitted May 5, 2016. Published September 20, 2016.
Math Subject Classifications: 31A30, 31B30, 35J40.
Key Words: Elliptic equation; Robin-Cauchy problem;
self-adjoint operator; ill-posedness.
Show me the PDF file (207 KB), TEX file for this article.
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Berikbol T. Torebek Department of Differential Equations Department of Fundamental Mathematics Institute of Mathematics and Mathematical Modeling 125 Pushkin str., 050010 Almaty, Kazakhistan email: torebek@math.kz |
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