Stability for the damped wave equation with neutral delay
Sign Up to like & getrecommendations! Published in 2017 at "Mathematische Nachrichten"
DOI: 10.1002/mana.201600229
Abstract: Of concern is a wave equation with a distributed neutral delay. We prove that, despite the destructive nature of delays in general, solutions may go back to the equilibrium state in an exponential manner as… read more here.
Keywords: neutral delay; stability damped; delay; damped wave ... See more keywords
Damped wave systems on networks: exponential stability and uniform approximations
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DOI: 10.1007/s00211-017-0924-4
Abstract: We consider a damped linear hyperbolic system modeling the propagation of pressure waves in a network of pipes. Well-posedness is established via semi-group theory and the existence of a unique steady state is proven in… read more here.
Keywords: systems networks; networks exponential; wave systems; exponential stability ... See more keywords
Source Estimation for the Damped Wave Equation Using Modulating Functions Method: Application to the Estimation of the Cerebral Blood Flow
Sign Up to like & getrecommendations! Published in 2017 at "IFAC-PapersOnLine"
DOI: 10.1016/j.ifacol.2017.08.1356
Abstract: Abstract In this paper, a method based on modulating functions is proposed to estimate the Cerebral Blood Flow (CBF). The problem is written in an input estimation problem for a damped wave equation which is… read more here.
Keywords: blood flow; estimation; blood; damped wave ... See more keywords
Continuity of pullback attractors for evolution processes associated with semilinear damped wave equations with time-dependent coefficients
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DOI: 10.1016/j.jde.2021.06.036
Abstract: Abstract In this paper we consider the semilinear damped wave problem of the form { ( α ( t ) u t ) t − β ( t ) Δ u + γ ( t… read more here.
Keywords: processes associated; semilinear damped; evolution processes; pullback attractors ... See more keywords
Decay character and estimates for the damped wave equation
Sign Up to like & getrecommendations! Published in 2022 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2021.125548
Abstract: Abstract Properties concerning the decay of solutions to the linear damped wave equation are essential tools for studying decay and long time behaviour of solutions to their semilinear and nonlinear counterparts. In this article we… read more here.
Keywords: damped wave; decay character; wave equation;
Effective dynamics for a class of stochastic weakly damped wave equation with a fast oscillation
Sign Up to like & getrecommendations! Published in 2023 at "Journal of Mathematical Physics"
DOI: 10.1063/5.0137730
Abstract: The purpose of this paper is to consider the effective dynamic behavior of a class of stochastic weakly damped wave equations with a fast oscillation under the non-Lipschitz condition. We show that the slow component… read more here.
Keywords: damped wave; class stochastic; stochastic weakly; weakly damped ... See more keywords
Invariant measures for the stochastic strongly damped wave equation
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DOI: 10.1063/5.0189165
Abstract: In this paper, a stochastic strongly damped wave equation with polynomial drift and diffusion terms is studied. First we prove there exists a unique solution for this equation by using a truncation method. Then, we… read more here.
Keywords: equation; strongly damped; stochastic strongly; wave equation ... See more keywords
Regularization of initial inverse problem for strongly damped wave equation
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DOI: 10.1080/00036811.2017.1359560
Abstract: Abstract In this paper, we consider the problem of finding the function , from the final data and where is a linear, unbounded, self-adjoint and positive definite operator. This problem is known as the inverse… read more here.
Keywords: regularization initial; inverse problem; strongly damped; initial inverse ... See more keywords
Recovering a potential in damped wave equation from Dirichlet-to-Neumann operator
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DOI: 10.1088/1361-6420/abdb41
Abstract: The inverse problem of recovering the potential q(x) in the damped wave equation m(x)utt+μ(x)ut=r(x)uxx+q(x)u , (x, t) ∈ Ω T ≔ (0, ℓ) × (0, T) subject to the boundary conditions u(0, t) = ν(t),… read more here.
Keywords: potential damped; recovering potential; damped wave; equation ... See more keywords
On a one-dimensional time-fractionally damped wave equation with a singular potential
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DOI: 10.1088/1402-4896/ad5656
Abstract: A nonlinear time-fractionally damped wave equation with an inverse-square potential posed on the interval (0, 1) is investigated. The time-fractionally derivative is considered in the Caputo sense. A weight function of the form x −σ… read more here.
Keywords: fractionally damped; time; wave equation; damped wave ... See more keywords
On the Symmetries and Conservation Laws of the Multidimensional Nonlinear Damped Wave Equations
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DOI: 10.1155/2017/9401205
Abstract: We carry out a classification of Lie symmetries for the ()-dimensional nonlinear damped wave equation with variable damping. Similarity reductions of the equation are performed using the admitted Lie symmetries of the equation and some… read more here.
Keywords: nonlinear damped; symmetries conservation; laws multidimensional; multidimensional nonlinear ... See more keywords