Email this article Criterion for the solvability of the cauchy problem for an abstract Euler–Poisson–Darboux equation
- Authors: Glushak A.V.1, Pokruchin O.A.1
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Affiliations:
- Belgorod National Research University
- Issue: Vol 52, No 1 (2016)
- Pages: 39-57
- Section: Partial Differential Equations
- URL: https://journals.rcsi.science/0012-2661/article/view/153606
- DOI: https://doi.org/10.1134/S0012266116010043
- ID: 153606
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Abstract
We consider the Cauchy problem for an abstract Euler–Poisson–Darboux equation in a Banach space and prove a necessary and a sufficient condition for the solvability of this problem. The conditions are stated in terms of an estimate for the norm of a fractional power of the resolvent and its derivatives. The properties of solutions are established, and examples are given.
About the authors
A. V. Glushak
Belgorod National Research University
Author for correspondence.
Email: aleglu@mail.ru
Russian Federation, Belgorod
O. A. Pokruchin
Belgorod National Research University
Email: aleglu@mail.ru
Russian Federation, Belgorod
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