Related papers: Local energy decay for Lipschitz wavespeeds
Before proving (unconditional) energy stability for gradient flows, most existing studies either require a strong Lipschitz condition regarding the non-linearity or certain $L^{\infty}$ bounds on the numerical solutions (the maximum…
We prove decay with respect to some Lebesgue norms for a class of Schr\"odinger equations with non-local nonlinearities by showing new Morawetz inequalities and estimates. As a byproduct, we obtain large-data scattering in the energy space…
A new decomposition for frequency-localized solutions to the Schrodinger equation is given which describes the evolution of the wavefunction using a weighted sum of Lipschitz tubes. As an application of this decomposition, we provide a new…
This paper aims at proving the local boundedness and continuity of solutions of the heat equation in the context of Dirichlet spaces under some rather weak additional assumptions. We consider symmetric local regular Dirichlet forms which…
In this paper, we embark on a captivating exploration of the stabilization of locally transmitted problems within the realm of two interconnected wave systems. To begin, we wield the formidable Arendt-Batty criteria\cite{AW} to affirm the…
In this paper we prove observability estimates for 1-dimensional wave equations with non-Lipschitz coefficients. For coefficients in the Zygmund class we prove a "classical" observability estimate, which extends the well-known observability…
We calculate the rate of ocean waves energy dissipation due to whitecapping by numerical simulation of deterministic phase resolving model for dynamics of ocean surface. Two independent numerical experiments are performed. First, we solve…
We establish a local boundedness estimate for weak subsolutions to a doubly nonlinear parabolic fractional $p$-Laplace equation. Our argument relies on energy estimates and a parabolic nonlocal version of De Giorgi's method. Furthermore, by…
We study the damped wave equation with a damping coefficient which is possibly singular and unbounded at infinity. In general, zero belongs to the spectrum of the corresponding generator, which prevents a uniform (exponential) decay for the…
We study the conformal wave equation $\square_g \psi + \frac{2}{l^2} \psi = 0$ on 4-dimensional Schwarzschild--Anti de Sitter spacetimes under dissipative boundary conditions. We prove boundedness and decay of the non-degenerate energy of…
In this paper we study the evolution of the wave function with the system size in a locally periodic structure. In particular we analyse the dependence of the wave function with the number of unit cells, which also reflects information…
In this paper we study the Cauchy problem for the wave equations for sums of squares of left invariant vector fields on compact Lie groups and also for hypoelliptic homogeneous left-invariant differential operators on graded Lie groups (the…
In this note, we are interested in the problem of scattering by J strictly convex obstacles satisfying a no-eclipse condition in dimension 2. We use the result of a previous article of the author to obtain polynomial resolvent estimates in…
In this paper we study the behaviors of the energy of solutions of the wave equations with localized nonlinear damping in exterior domains.
In this paper, we study the energy decay for the thermoelastic Bresse system in the whole line with two different dissipative mechanism, given by heat conduction (Types I and III). We prove that the decay rate of the solutions are very…
A strong local form of the ``4/3-law'' in turbulent flow has been proved recently by Duchon and Robert for a triple moment of velocity increments averaged over both a bounded spacetime region and separation vector directions, and for energy…
The fractional wave equation governs the propagation of mechanical diffusive waves in viscoelastic media which exhibits a power-law creep, and consequently provided a physical interpretation of this equation in the framework of dynamic…
We consider the Cauchy problem for the weakly dissipative wave equation $$ \bx v+\frac\mu{1+t}v_t=0, \qquad x\in\R^n,\quad t\ge 0, $$ parameterized by $\mu>0$, and prove a representation theorem for its solution using the theory of special…
We develop a general energy method for proving the optimal time decay rates of the solutions to the dissipative equations in the whole space. Our method is applied to classical examples such as the heat equation, the compressible…
We discuss a Lipschitz truncation technique for parabolic double-phase problems of $p$-Laplace type in order to prove energy estimates and uniqueness results for the Dirichlet problem. Moreover, we show existence for a non-homogeneous…