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Solvability of loaded linear evolution equations with a degenerate operator at the derivative

Authors: V. E. Fedorov and L. V. Borel
Translated by: the authors
Original publication: Algebra i Analiz, tom 26 (2014), nomer 3.
Journal: St. Petersburg Math. J. 26 (2015), 487-497
MSC (2010): Primary 35R09, 34K30, 45K05
Published electronically: March 20, 2015
MathSciNet review: 3289182
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Abstract | References | Similar Articles | Additional Information

Abstract: The methods of degenerate semigroups of operators and the theorem on contraction mappings are used for the search of unique solvability conditions for the Cauchy problem and the generalized Showalter problem for a class of loaded linear differential operator equations of the first order with degenerate operator at the derivative. The general results obtained are applied to the study of initial boundary value problems for loaded partial differential equations not solvable with respect to the time derivative.

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Additional Information

V. E. Fedorov
Affiliation: Laboratory of Quantum Topology, Chelyabinsk State University, Kashirin Brothers Str. 129, Chelyabinsk 454001, Russia

L. V. Borel
Affiliation: Division of Mathematical Analysis, Chelyabinsk State University, Kashirin Brothers Str. 129, Chelyabinsk 454001, Russia

Keywords: Loaded equation, Sobolev type equation, degenerate operator semigroup
Received by editor(s): January 10, 2014
Published electronically: March 20, 2015
Additional Notes: Supported by the Laboratory of Quantum Topology of Chelyabinsk State University (grant no. 14.Z50.31.0020 of the Government of the Russian Federation)
Article copyright: © Copyright 2015 American Mathematical Society