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Inverse problem with a time‐integral condition for a fractional diffusion equation
Author(s) -
Lopushanska Halyna,
Lopushansky Andriy
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5587
Subject(s) - mathematics , overdetermination , mathematical analysis , inverse problem , initial value problem , type (biology) , diffusion equation , inverse , fractional calculus , integral equation , diffusion , geometry , ecology , philosophy , physics , economy , epistemology , economics , biology , service (business) , thermodynamics
We find the conditions for the unique solvability of the inverse problem for a time‐fractional diffusion equation with Schwarz‐type distributions in the right‐hand sides. This problem is to find a generalized solution of the Cauchy problem and an unknown space‐dependent part of an equation's right‐hand side under a time‐integral overdetermination condition.