Identifications for General Degenerate Problems of Hyperbolic Type in Hilbert Spaces

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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.

About the authors

A Favini

Universita` di Bologna

Email: angelo.favini@unibo.it

G Marinoschi

Institute of Statistical Mathematics and Applied Mathematics

Email: gabimarinoschi@yahoo.com

H Tanabe

Hirai Sanso

Email: h7tanabe@jttk.zaq.ne.jp

Ya Yakubov

Tel-Aviv University

Email: yakubov@post.tau.ac.il

References

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