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Control problems for weakly coupled systems with memory
Paola Loreti,Daniela Sforza +1 more
TL;DR: In this article, the authors investigate control problems for wave-Petrovsky coupled systems in the presence of memory terms and prove Ingham type estimates, and hence reachability results.
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Abstract: We investigate control problems for wave-Petrovsky coupled systems in the presence of memory terms. By writing the solutions as Fourier series, we are able to prove Ingham type estimates, and hence reachability results. Our findings have applications in viscoelasticity theory and linear acoustic theory.
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Abstract Volterra integrodifferential equations with applications to parabolic models with memory
Bruno de Andrade,Arlúcio Viana +1 more
TL;DR: This paper presents a result on unique continuation and a blow-up alternative for an $$epsilon $$ϵ-regular mild solution of (1, 2) and applies the results to three interesting models: Navier–Stokes equations with memory, diffusion equations withmemory and a strongly damped plate equation with memory.
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Integrodifferential equations with applications to a plate equation with memory
Bruno de Andrade,Arlúcio Viana +1 more
TL;DR: In this paper, local existence, uniqueness, and continuous dependence of an abstract integrodifferential equation were studied. And they also presented a result on unique continuation and a blow-up alternative for mild solutions of the integro-differential equation.
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Numerical solution of a control problem for ordinary differential equations with multipoint integral condition
TL;DR: In this paper, a linear boundary value problem with a parameter for ordinary differential equations with multipoint integral condition is investigated, where the method of parameterization is used for solving the considered problem.
Partial observability of a wave-Petrovsky system with memory
Paola Loreti,Daniela Sforza +1 more
TL;DR: In this article, partial observability results for coupled systems with memory terms were shown by means of non-harmonic analysis techniques, and Theorem 3.2 and 3.7 below.
2
References
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Evolutionary integral equations and applications
Jan Prüss
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TL;DR: In this article, the authors deal with evolutionary systems whose equation of state can be formulated as a linear Volterra equation in a Banach space, where the main feature of the kernels involved is that they consist of unbounded linear operators.
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Controllability and Stabilizability Theory for Linear Partial Differential Equations: Recent Progress and Open Questions
TL;DR: The current state of controllability and observability theories for linear PDEs is summarized in this article.However, the state of the art for observability and controllable PDE theories is limited.
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Volterra Integral and Functional Equations
Gustaf Gripenberg,Stig-Olof Londen,Olof J. Staffans +2 more
- 30 Mar 1990
TL;DR: In this article, the authors present an overview of linear and nonlinear theory and frequency domain methods for nonlinear solutions of linear non-convolutional equations, including continuous dependence, differentiability and uniqueness.
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An Introduction to Seismology, Earthquakes, and Earth Structure
Seth Stein,Michael E. Wysession +1 more
- 01 Jan 2002
TL;DR: Inverse problems are solved by solving selected odd-numbered problems as mentioned in this paper, which is a special case of the problem we consider in this paper, where the authors consider the problem of finding a solution to the odd-number problem.
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