Ravi P. Agarwal, Umida Baltaeva, Florence Hubert, Boburjon Khasanov
Abstract:
This work is devoted to the unique solvability of the direct and
inverse problems for a multidimensional heat equation with a
fractional load in Holder spaces.
In the problem under consideration, the loaded term is in
the form of a fractional integral operator for the time variable.
We prove the existence and uniqueness of the solution to these
problems by the contraction mapping theorem and the theory of
integral equations.
Submitted August 15, 2024. Published October 23, 2024.
Math Subject Classifications: 35K15, 35R30.
Key Words: Heat equation; Cauchy problem; inverse problem; loaded equation; fractional operator.
DOI: 10.58997/ejde.2024.64
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Ravi P. Agarwal Emeritus Research Professor Department of Mathematics and Systems Engineering Florida Institute of Technology Melbourne, FL 32901, USA email: agarwalr@fit.edu |
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Umida Baltaeva Department of Applied Mathematics and Mathematical Physics Urgench State University Urgench, Uzbekistan email: umida_baltayeva@mail.ru |
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Florence Hubert Aix-Marseille Universite CNRS, I2M, Marseille, France email: florence.hubert@univ-amu.fr |
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Boburjon Khasanov Khorezm Mamun Academy Khorezm, Uzbekistan email: xasanovboburjon.1993@gmail.com |
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