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Of primary interest in this paper is the numerical approximation of a time dependent fractional, in space, diffusion equation where the domain is assumed to be nonhomogeneous, having different axial diffusion coefficients. This work is…

Numerical Analysis · Mathematics 2026-05-12 T. Catoe , V. J. Ervin

A one-dimensional wave propagation through elastically asymmetric media is investigated. A class of metamaterials possessing an arbitrary elastic asymmetry is proposed. This asymmetry results in different wave speeds of tensile and…

Soft Condensed Matter · Physics 2021-01-26 Vladislav A. Yastrebov

We consider several models of nonlinear wave equations subject to very strong damping and quasi-periodic external forcing. This is a singular perturbation, since the damping is not the highest order term. We study the existence of response…

Analysis of PDEs · Mathematics 2015-01-27 Renato C. Calleja , Alessandra Celletti , Livia Corsi , Rafael de la Llave

A weak formulation for the so-called "semilinear strongly damped wave equation with constraint" is introduced and a corresponding notion of solution is defined. The main idea in this approach consists in the use of duality techniques in…

Analysis of PDEs · Mathematics 2015-03-09 Elena Bonetti , Elisabetta Rocca , Riccardo Scala , Giulio Schimperna

In this article, we investigate the blow-up for local solutions to a semilinear wave equation in the generalized Einstein - de Sitter spacetime with nonlinearity of derivative type. More precisely, we consider a semilinear damped wave…

Analysis of PDEs · Mathematics 2022-06-22 Makram Hamouda , Mohamed Ali Hamza , Alessandro Palmieri

We consider a strictly hyperbolic, genuinely nonlinear system of conservation laws in one space dimension. A sharp decay estimate is proved for the positive waves in an entropy weak solution. The result is stated in terms of a partial…

Analysis of PDEs · Mathematics 2007-05-23 Alberto Bressan , Tong Yang

In this series of papers, we investigate the spreading and vanishing dynamics of time almost periodic diffusive KPP equations with free boundaries. Such equations are used to characterize the spreading of a new species in time almost…

Analysis of PDEs · Mathematics 2015-07-08 Fang Li , Xing Liang , Wenxian Shen

This paper focuses on the study of semilinear fractional diffusion-wave equations in the context of critical nonlinearities. Firstly, we address the issue of local well-posedness for the problem, examine spatial regularity, and the…

Analysis of PDEs · Mathematics 2026-02-09 Masterson Costa , Claudio Cuevas , Bruno de Andrade

The compressible Navier-Stokes-Poisson system takes the form of usual Navier-Stokes equations coupled with the self-consistent Poisson equation, which is used to simulate the transport of charged particles under the electric field of…

Analysis of PDEs · Mathematics 2018-05-30 Wei Xuan Shi , Jiang Xu

This paper discusses aspects of the second order hyperbolic partial differential equation associated with the ideal lossless string under tension and it's relationship to two discrete models. These models are finite differencing in the time…

Computational Physics · Physics 2007-05-23 Georg Essl

We propose a model for frequency-dependent damping in the linear wave equation. After proving well-posedness of the problem, we study qualitative properties of the energy. In the one-dimensional case, we provide an explicit analysis for…

Analysis of PDEs · Mathematics 2025-03-06 Francesco Maddalena , Gianluca Orlando

This paper is concerned with weighted energy estimates and diffusion 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…

Analysis of PDEs · Mathematics 2016-11-24 Motohiro Sobajima , Yuta Wakasugi

In this paper, we study the Navier-Stokes-Korteweg equations governed by the evolution of compressible fluids with capillarity effects. We first investigate the global well-posedness of solution in the critical Besov space for large initial…

Analysis of PDEs · Mathematics 2024-04-16 Zihao Song

This paper is devoted to the study of some qualitative and quantitative aspects of nonlinear propagation phenomena in diffusive media. More precisely, we consider the case a reaction-diffusion equation in a periodic medium with…

Analysis of PDEs · Mathematics 2009-04-27 Francois Hamel , Yannick Sire

In this paper, we show that all non-trivial solutions of a broad class of nonlinear dispersive equations, whose linear evolution is governed by a dispersion relation under minimal regularity assumptions, cannot remain compactly supported…

Analysis of PDEs · Mathematics 2026-02-23 Brian Choi , Steven Walton

In this paper, we are concerned with a time-dependent transmission problem for a thermo-piezoelectric elastic body immersed in a compressible fluid. It is shown that the problem can be treated by the boundary-field equation method, provided…

Analysis of PDEs · Mathematics 2021-05-28 George C. Hsiao , Tonatiuh Sánchez-Vizuet

Turbulent relative dispersion is studied theoretically with a focus on the evolution of probability distribution of the relative separation of two passive particles. A finite separation speed and a finite correlation of relative velocity,…

Chaotic Dynamics · Physics 2007-05-23 Takeshi Ogasawara , Sadayoshi Toh

We introduce a novel framework for the analysis of linear wave equations on nonstationary asymptotically flat spacetimes, under the assumptions of mode stability and absence of zero energy resonances for a stationary model operator. Our…

Analysis of PDEs · Mathematics 2023-03-01 Peter Hintz

We examine an extension to the theory of Gaussian wave packet dynamics in a one-dimensional potential by means of a sequence of time dependent displacement and squeezing transformations. Exact expressions for the quantum dynamics are found,…

Atomic Physics · Physics 2009-10-31 B. M. Garraway

This paper studies time-dependent electromagnetic scattering from metamaterials that are described by dispersive material laws. We consider the numerical treatment of a scattering problem in which a dispersive material law, for a causal and…

Numerical Analysis · Mathematics 2023-11-08 Jörg Nick , Selina Burkhard , Christian Lubich