Electron. J. Differential Equations,
Vol. 2016 (2016), No. 252, pp. 19.
A method for solving illposed RobinCauchy problems for secondorder
elliptic equations in multidimensional cylindrical domains
Berikbol T. Torebek
Abstract:
In this article we consider the RobinCauchy problem for multidimensional
elliptic equations in a cylindrical domain. The method of spectral
expansion in eigenfunctions of the RobinCauchy problem for equations
with deviating argument establishes a criterion of the strong solvability
of the considered RobinCauchy problem. It is shown that the illposedness
of the RobinCauchy problem is equivalent to the existence of an isolated
point of the continuous spectrum for a selfadjoint operator with the
deviating argument.
Submitted
Submitted May 5, 2016. Published September 20, 2016.
Math Subject Classifications: 31A30, 31B30, 35J40.
Key Words: Elliptic equation; RobinCauchy problem;
selfadjoint operator; illposedness.
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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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