相关论文: Finite speed of propagation for the 2- and 3-dimen…

We prove finite speed of propagation for stochastic porous media equations perturbed by linear multiplicative space-time rough signals. Explicit and optimal estimates for the speed of propagation are given. The result applies to any…

We prove the existence of global solutions to the Cauchy problem for noncommutative nonlinear wave equations in arbitrary even spatial dimensions where the noncommutativity is only in the spatial directions. We find that for existence there…

We prove the existence of infinite energy global solutions of the cubic wave equation in dimension greater than 3. The data is a typical element on the support of suitable probability measures.

Finite propagation speed properties in mathematical elastic and viscoelastic models are fundamental in many applications where the data exhibits propagating fronts. We note particularly that this property is observed in biomechanical…

Global smooth solutions to the initial value problem for systems of nonlinear wave equations with multiple propagation speeds will be constructed in the case of small initial data and nonlinearities satisfying the null condition.

This note is concerned with proving the finite speed of propagation for some non-local porous medium equation by adapting arguments developed by Caffarelli and V\'azquez (2010).

A detailed investigation is presented of a simple unidirectional finite-energy solution of the 3D wave equation. Its asymptotics as a spatial point runs to infinity with the wave propagations speed is a standard spherical wave as z < 0,…

We prove maximal speed estimates for nonlinear quantum propagation in the context of the Hartree equation. More precisely, under some regularity and integrability assumptions on the pair (convolution) potential, we construct a set of energy…

We study the two-dimensional wave equation with cubic nonlinearity posed on $\mathbb R^2$, with space-time white noise forcing. After a suitable renormalisation of the nonlinearity, we prove global well-posedness for this equation for…

We show that a double degenerate thin film equation, which originated from modeling of viscous coating flow on a spherical surface, has finite speed of propagation for nonnegative strong solutions and hence there exists an interface or free…

The peridynamic analogue of the wave equation does not have finite speed propogation. We show, for one dimensional linear peridynamics, that solutions do nonetheless satisfy estimates analogous to those satisfied by solutions of the wave…

We prove pointwise-in-time dispersive decay for solutions to the energy-critical nonlinear wave equation in spatial dimension $d = 3$.

This paper is concerned with pulsating waves for multi-dimensional reaction-diffusion equations in spatially periodic media. First, assuming the existence of pulsating waves connecting two linearly stable steady states, we study the…

We consider the Cauchy problem for systems of nonlinear wave equations with multiple propagation speeds in three space dimensions. Under the null condition for such systems, the global existence of small amplitude solutions is known. In…

In this paper we prove a global spacetime bound for the quintic, nonlinear wave equation in three dimensions. This bound depends on the $L_{t}^{\infty} L_{x}^{2}$ and $L_{t}^{\infty} \dot{H}^{2}$ norms of the solution to the quintic…

We propose some modification of Maxwell's equations describing mediums which electric and magnetic properties are changed essentially after interaction with outer electromagnetic field. We show for such mediums that electromagnetic waves…

In this paper, the one-dimensional time-fractional diffusion-wave equation with the fractional derivative of order $1 \le \alpha \le 2$ is revisited. This equation interpolates between the diffusion and the wave equations that behave quite…

In this paper, the unidirectional pulse propagation equation generalized to structured media is derived. A fast modal transform linking the spatio-temporal representation of the field and its modal distribution is presented. This transform…

We consider finite-energy solutions to the defocusing nonlinear wave equation in two dimensional space. We prove that almost all energy moves to the infinity at almost the light speed as time tends to infinity. In addition, the…

We consider an abstract wave equation with a propagation speed that depends only on time. We investigate well-posedness results with finite derivative loss in the case where the propagation speed is smooth for positive times, but…