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

Fedorov, V.; Borel, L.

doi:10.1090/S1061-0022-2015-01348-4

Solvability of loaded linear evolution equations with a degenerate operator at the derivative
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by V. E. Fedorov and L. V. Borel
Translated by: the authors

St. Petersburg Math. J. 26 (2015), 487-497

DOI: https://doi.org/10.1090/S1061-0022-2015-01348-4

Published electronically: March 20, 2015

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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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