Identifications for General Degenerate Problems of Hyperbolic Type in Hilbert Spaces

A Favini; G Marinoschi; H Tanabe; Ya Yakubov

doi:10.22363/2413-3639-2018-64-1-194-210

by A Favini, G Marinoschi, H Tanabe, Ya Yakubov

Published in Contemporary Mathematics. Fundamental Directions by Peoples' Friendship University of Russia.

2018 Volume 64, p194-210

Abstract

In a Hilbert space X, we consider the abstract problem M∗ddt(My(t))=Ly(t)+f(t)z,0≤t≤τ,My(0)=My0, where L is a closed linear operator in X and M∈L(X) is not necessarily invertible, z∈X. Given the additional information Φ[My(t)]=g(t) wuth Φ∈X∗, g∈C1([0,τ];C). We are concerned with the determination of the conditions under which we can identify f∈C([0,τ];C) such that y be a strict solution to the abstract problem, i.e., My∈C1([0,τ];X), Ly∈C([0,τ];X). A similar problem is considered for general second order equations in time. Various examples of these general problems are given.
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Date 2018-12-15

DOI 10.22363/2413-3639-2018-64-1-194-210

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