On a time nonlocal problem for inhomogeneous evolution equations

Федоров, В. Е.; Иванова, Наталья Дмитриевна; Fedorova, Yu. Yu.

doi:10.1134/s0037446614040144

Cited by 4 publications

(1 citation statement)

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“…A. Vasin concerning nonlinear inverse problems for evolution equations that are solved with respect to the time derivative. Based on ideas of these works, a class of nonlinear inverse problems for degenerate evoltion equations was researched in before. By the results on the unique solvability of the abstract problem, obtained by the authors in , the existence of a unique classical solution for the Oskolkov's system inverse problem is proved.…”

Section: Introductionmentioning

confidence: 99%

Inverse problem for Oskolkov's system of equations

Fedorov

Иванова

2015

Math Methods in App Sciences

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The inverse problem with unknown source function is studied for the nonlinear Oskolkov's system of partial differential equations that describes the dynamics of viscoelastic Kelvin–Voigt fluid. It is reduced to the problem for a first order semilinear ordinary differential equation with operator coefficients in Banach spaces. The main difficulty of the problem is a presence of the operator with a nontrivial kernel at the derivative. By the results on the unique solvability of the abstract problem, obtained by the authors before, the existence of a unique classical solution for the Oskolkov's system inverse problem is proved. Copyright © 2015 John Wiley & Sons, Ltd.

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Section: Introductionmentioning

confidence: 99%