Related papers: Wave equations with mass and dissipation

We consider wave models with lower order terms and recollect some recent results on energy and dispersive estimates for their solution based on symbolic type estimates for coefficients and partly stabilisation conditions. The exposition is…

In this paper, we pursue our series of papers aiming to show the applicability of the concept of very weak solutions. We consider a wave model with irregular position dependent mass and dissipation terms, in particular, allowing for…

In this paper we consider a singular wave equation with distributional and more singular non-distributional coefficients and develop tools and techniques for the phase-space analysis of such problems. In particular we provide a detailed…

Motivated by numerically modeling surface waves for inviscid Euler equations, we analyze linear models for damped water waves and establish decay properties for the energy for sufficiently regular initial configurations. Our findings give…

A model is presented for the characterization of dissipative effects on highly nonlinear waves in one-dimensional dry granular media. The model includes three terms: Hertzian, viscoelastic, and a term proportional to the square of the…

In this article we shall go over recent work in proving dispersive and Strichartz estimates for the Dirichlet-wave equation. We shall discuss applications to existence questions outside of obstacles and discuss open problems.

In this work we consider weakly non-radiative solutions to both linear and non-linear wave equations. We first characterize all weakly non-radiative free waves, without the radial assumption. Then in dimension 3 we show that the initial…

We consider a layer of an inviscid fluid with free surface which is subject to vertical high-frequency vibrations. We derive three asymptotic systems of equations that describe slowly evolving (in comparison with the vibration frequency)…

In this work, we investigate mathematical models for electromagnetic wave propagation in dispersive isotropic media. We emphasize the link between physical requirements and mathematical properties of the models. A particular attention is…

In this paper we derive some new weakly nonlinear asymptotic models describing viscous waves in deep water with or without surface tension effects. These asymptotic models take into account several different dissipative effects and are…

Energy nonconservation is a serious problem of dynamical collapse theories. In this paper, we propose a discrete model of energy-conserved wavefunction collapse. It is shown that the model is consistent with existing experiments and our…

In this paper we consider an acoustic problem of wave propagation through a discontinuous medium. The problem is reduced to the dissipative wave equation with distributional dissipation. We show that this problem has a so-called very weak…

We consider the wave equation with a damping term on a partially rectangular planar domain, assuming that the damping is concentrated close to the non-rectangular part of the domain. Polynomial decay estimates for the energy of the solution…

We consider semilinear wave equations with small initial data in two space dimensions. For a class of wave equations with cubic nonlinearity, we show the global existence of small amplitude solutions, and give an asymptotic description of…

In this paper we focus on the global-in-time existence and the pointwise estimates of solutions to the initial value problem for the semilinear dissipative wave equation in multi-dimensions. By using the method of Green function combined…

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…

In this paper we consider energy decay estimates for the Cauchy problems of dissipative wave equations with time dependent coefficients, in particular, the coefficients consisting of weak dissipation and very fast oscillating terms. For…

In this paper, we study the asymptotic behavior of solutions to the wave equation with damping depending on the space variable and growing at the spatial infinity. We prove that the solution is approximated by that of the corresponding heat…

The paper studies the interaction of a longitudinal wave with transverse waves in general isotropic and unconstrained hyperelastic materials, including the possibility of dissipation. The dissipative term chosen is similar to the classical…

We study the global existence and decay estimates for nonlinear wave equations with the space-time dependent dissipative term in an exterior domain. The linear dissipative effect may vanish in a compact space region. Moreover the nonlinear…