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Author Banks, H. T. ♦ Pedersen, M.
Source CiteSeerX
Content type Text
File Format PDF
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Reasonable Assumption ♦ Vd Vd ♦ Abstract Differential Operator Form ♦ Time-dependent Sesquilinear ♦ Abstract Hyperbolic Model ♦ Dense Injection ♦ Inverse Problem ♦ Associated Duality Product ♦ Hilbert Space ♦ Finite Element Type Approximation ♦ Weak Formulation ♦ Unique Solution ♦ Several Important Kind ♦ Associated Inverse Problem ♦ Shell Equation ♦ Time Dependent Stiffness
Abstract inverse problems. 1 Abstract. In this paper we investigate the abstract hyperbolic model with time dependent stiffness and damping given by ⟨ü(t), ψ⟩V ∗,V + d(t; ˙u(t), ψ) + a(t; u(t), ψ) = ⟨f(t), ψ⟩V ∗,V where V ⊂ VD ⊂ H ⊂ V ∗ D ⊂ V ∗ are Hilbert spaces with continuous and dense injections, where H is identified with its dual and ⟨·, · ⟩ denotes the associated duality product. We show under reasonable assumptions on the time-dependent sesquilinear forms a(t; ·, ·) : V × V → C and d(t; ·, ·) : VD × VD → C that this model allows a unique solution and that the solution depends continuously on the data of the problem. We also consider well-posedness as well as finite element type approximations in associated inverse problems. The problem above is a weak formulation that includes models in abstract differential operator form that include plate, beam and shell equations with several important kinds of damping. 2 1
Educational Role Student ♦ Teacher
Age Range above 22 year
Educational Use Research
Education Level UG and PG ♦ Career/Technical Study
Learning Resource Type Article
Publisher Date 2008-01-01