The Experts below are selected from a list of 12867 Experts worldwide ranked by ideXlab platform
A. D. Hassiotis - One of the best experts on this subject based on the ideXlab platform.
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To Appear in Monthly Weather Review AN UPPER GRAVITY-WAVE ABSORBING LAYER FOR NWP APPLICATIONS
2015Co-Authors: J. B. Klemp, J. Dudhia, A. D. HassiotisAbstract:Although the use of a Damping layer near the top of a computational model domain has proven effective in absorbing upward-proagating gravity-wave energy in idealized simulations, this technique has been less successful in real atmospheric applications. Here, a new technique is proposed for nonhydrostatic model equations that are solved using split-explicit time integration techniques. In this method, an implicit Rayleigh Damping Term is applied only to the vertical velocity, as a final adjustment at the end of each small (acoustic) time step. The adjustment is equivalent to including an implicit Rayleigh Damping Term in the vertical momentum equation together with an implicit vertical diffusion of w, and could be applied in this manner in other time integration schemes. This implicit Damping for the vertical velocity is unconditionally stable and remains effective even for hydrostatic gravity waves. The good absorption characteristics of this layer across a wide range of horizontal scales are confirmed though analysis of the linear wave equation and numerical mountain-wave simulations, and through simulations of an idealized squall line and of mountain waves over the Colorado Rocky Mountains. 1
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an upper gravity wave absorbing layer for nwp applications
Monthly Weather Review, 2008Co-Authors: J. B. Klemp, J. Dudhia, A. D. HassiotisAbstract:Although the use of a Damping layer near the top of a computational model domain has proven effective in absorbing upward-propagating gravity-wave energy in idealized simulations, this technique has been less successful in real atmospheric applications. Here, a new technique is proposed for nonhydrostatic model equations that are solved using split-explicit time-integration techniques. In this method, an implicit Rayleigh Damping Term is applied only to the vertical velocity, as a final adjustment at the end of each small (acoustic) time step. The adjustment is equivalent to including an implicit Rayleigh Damping Term in the vertical momentum equation together with an implicit vertical diffusion of w, and could be applied in this manner in other time-integration schemes. This implicit Damping for the vertical velocity is unconditionally stable and remains effective even for hydrostatic gravity waves. The good absorption characteristics of this layer across a wide range of horizontal scales are confirmed through analysis of the linear wave equation and numerical mountain-wave simulations, and through simulations of an idealized squall line and of mountain waves over the Colorado Rocky Mountains.
Wenjun Liu - One of the best experts on this subject based on the ideXlab platform.
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a note on blow up of solutions for a class of fourth order wave equation with viscous Damping Term
Applicable Analysis, 2018Co-Authors: Weifan Zhao, Wenjun LiuAbstract:In this note, we study a class of fourth-order wave equation with viscous Damping Term and illuminate that the condition on the relationship between and p in Theorem 4.2 of Xu et al. (Appl Anal. 2013;92(7):1403–1416) can be removed. This is achieved by adopting and modifying the so-called concavity method. Furthermore, we establish a blow-up result for positive initial energy without the relationship between and p as well.
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general decay for a viscoelastic kirchhoff equation with balakrishnan taylor Damping dynamic boundary conditions and a time varying delay Term
Evolution Equations and Control Theory, 2017Co-Authors: Wenjun Liu, Biqing Zhu, Danhua WangAbstract:In this paper, we consider a viscoelastic Kirchhoff equation with Balakrishnan-Taylor Damping, dynamic boundary conditions and a time-varying delay Term acting on the boundary. By using the Faedo-Galerkin approximation method, we first prove the well-posedness of the solutions. By introducing suitable energy and perturbed Lyapunov functionals, we then prove the general decay results, from which the usual exponential and polynomial decay rates are only special cases. To achieve these results, we consider the following two cases according to the coefficient α of the strong Damping Term: for the presence of the strong Damping Term (α>0), we use the strong Damping Term to control the time-varying delay Term, under a restriction of the size between the time-varying delay Term and the strong Damping Term; for the absence of the strong Damping Term (α=0), we use the viscoelasticity Term to control the time-varying delay Term, under a restriction of the size between the time-varying delay Term and the kernel function.
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general decay rate estimate for a viscoelastic equation with weakly nonlinear time dependent dissipation and source Terms
Journal of Mathematical Physics, 2009Co-Authors: Wenjun LiuAbstract:A viscoelastic wave equation in canonical form with weakly nonlinear time-dependent dissipation and source Terms is investigated in this paper. For a wider class of relaxation functions and without imposing any restrictive growth assumption on the Damping Term at the origin, we establish an explicit and general energy decay rate result.
Yuta Wakasugi - One of the best experts on this subject based on the ideXlab platform.
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sharp lifespan estimates of blowup solutions to semilinear wave equations with time dependent effective Damping
Journal of Hyperbolic Differential Equations, 2019Co-Authors: Masahiro Ikeda, Motohiro Sobajima, Yuta WakasugiAbstract:We consider the initial value problem for a semi-linear wave equation with a time-dependent effective Damping Term. The interest is the behavior of lifespan of solutions in view of the asymptotic p...
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weighted energy estimates for wave equation with space dependent Damping Term for slowly decaying initial data
Communications in Contemporary Mathematics, 2019Co-Authors: Motohiro Sobajima, Yuta WakasugiAbstract:This paper is concerned with weighted energy estimates for solutions to wave equation ∂t2u − Δu + a(x)∂ tu = 0 with space-dependent Damping Term a(x) = |x|−α (α ∈ [0, 1]) in an exterior domain Ω ha...
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weighted energy estimates for wave equation with space dependent Damping Term for slowly decaying initial data
arXiv: Analysis of PDEs, 2017Co-Authors: Motohiro Sobajima, Yuta WakasugiAbstract:This paper is concerned with weighted energy estimates for solutions to wave equation $\partial_t^2u-\Delta u + a(x)\partial_tu=0$ with space-dependent Damping Term $a(x)=|x|^{-\alpha}$ $(\alpha\in [0,1))$ in an exterior domain $\Omega$ having a smooth boundary. The main result asserts that the weighted energy estimates with weight function like polymonials are given and these decay rate are almost sharp, even when the initial data do not have compact support in $\Omega$. The crucial idea is to use special solution of $\partial_t u=|x|^{\alpha}\Delta u$ including Kummer's confluent hypergeometric functions.
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remarks on an elliptic problem arising in weighted energy estimates for wave equations with space dependent Damping Term in an exterior domain
arXiv: Analysis of PDEs, 2016Co-Authors: Motohiro Sobajima, Yuta WakasugiAbstract:This paper is concerned with weighted energy estimates and di usion phenomena for the initial-boundary problem of the wave equation with space-dependent Damping Term in an exterior domain. In this analysis, an elliptic problem was introduced by Todorova and Yordanov. This attempt was quite useful when the coeffcient of the Damping Term is radially symmetric. In this paper, by modifying their elliptic problem, we establish weighted energy estimates and di usion phenomena even when the coeffcient of the Damping Term is not radially symmetric.
J. B. Klemp - One of the best experts on this subject based on the ideXlab platform.
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To Appear in Monthly Weather Review AN UPPER GRAVITY-WAVE ABSORBING LAYER FOR NWP APPLICATIONS
2015Co-Authors: J. B. Klemp, J. Dudhia, A. D. HassiotisAbstract:Although the use of a Damping layer near the top of a computational model domain has proven effective in absorbing upward-proagating gravity-wave energy in idealized simulations, this technique has been less successful in real atmospheric applications. Here, a new technique is proposed for nonhydrostatic model equations that are solved using split-explicit time integration techniques. In this method, an implicit Rayleigh Damping Term is applied only to the vertical velocity, as a final adjustment at the end of each small (acoustic) time step. The adjustment is equivalent to including an implicit Rayleigh Damping Term in the vertical momentum equation together with an implicit vertical diffusion of w, and could be applied in this manner in other time integration schemes. This implicit Damping for the vertical velocity is unconditionally stable and remains effective even for hydrostatic gravity waves. The good absorption characteristics of this layer across a wide range of horizontal scales are confirmed though analysis of the linear wave equation and numerical mountain-wave simulations, and through simulations of an idealized squall line and of mountain waves over the Colorado Rocky Mountains. 1
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an upper gravity wave absorbing layer for nwp applications
Monthly Weather Review, 2008Co-Authors: J. B. Klemp, J. Dudhia, A. D. HassiotisAbstract:Although the use of a Damping layer near the top of a computational model domain has proven effective in absorbing upward-propagating gravity-wave energy in idealized simulations, this technique has been less successful in real atmospheric applications. Here, a new technique is proposed for nonhydrostatic model equations that are solved using split-explicit time-integration techniques. In this method, an implicit Rayleigh Damping Term is applied only to the vertical velocity, as a final adjustment at the end of each small (acoustic) time step. The adjustment is equivalent to including an implicit Rayleigh Damping Term in the vertical momentum equation together with an implicit vertical diffusion of w, and could be applied in this manner in other time-integration schemes. This implicit Damping for the vertical velocity is unconditionally stable and remains effective even for hydrostatic gravity waves. The good absorption characteristics of this layer across a wide range of horizontal scales are confirmed through analysis of the linear wave equation and numerical mountain-wave simulations, and through simulations of an idealized squall line and of mountain waves over the Colorado Rocky Mountains.
Daniel Lear - One of the best experts on this subject based on the ideXlab platform.
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on the asymptotic stability of stratified solutions for the 2d boussinesq equations with a velocity Damping Term
Mathematical Models and Methods in Applied Sciences, 2019Co-Authors: Angel Castro, Diego Cordoba, Daniel LearAbstract:We consider the 2D Boussinesq equations with a velocity Damping Term in a strip domain, with impermeable walls. In this physical scenario, where the Boussinesq approximation is accurate when densit...
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on the asymptotic stability of stratified solutions for the 2d boussinesq equations with a velocity Damping Term
arXiv: Analysis of PDEs, 2018Co-Authors: Angel Castro, Diego Cordoba, Daniel LearAbstract:We consider the 2D Boussinesq equations with a velocity Damping Term in a strip $\mathbb{T}\times[-1,1]$, with impermeable walls. In this physical scenario, where the \textit{Boussinesq approximation} is accurate when density/temperature variations are small, our main result is the asymptotic stability for a specific type of perturbations of a stratified solution. To prove this result, we use a suitably weighted energy space combined with linear decay, Duhamel's formula and "bootstrap" arguments.
