Related papers: Stochastic solutions of the wave equation
Solutions for a class of wave equations with effective potentials are obtained by a method of a Laplace-transform. Quasinormal modes appear naturally in the solutions only in a spatially truncated form; their coefficients are uniquely…
The goal of this work is to determine whole classes of solitary wave solutions general for wave equations.
A stochastic representation for the solutions of the Poisson-Vlasov equation is obtained. The representation involves both an exponential and a branching process. The stochastic representation, besides providing an alternative existence…
Based on a fundamental identity for stochastic hyperbolic-like operators, we derive in this paper a global Carleman estimate (with singular weight function) for stochastic wave equations. This leads to an observability estimate for…
In this paper, we establish the well-posedness of stochastic heat equations on moving domains, which amounts to a study of infinite dimensional interacting systems. The main difficulty is to deal with the problems caused by the time-varying…
We show that, contrary to the statements made by many authors, the backflow is not a nonclassical effect. The backflow is a characteristic feature of solutions of the wave equations: quantum and classical. We present simple solutions of the…
We consider the stochastic Swift-Hohenberg equation on a large domain near its change of stability. We show that, under the appropriate scaling, its solutions can be approximated by a periodic wave, which is modulated by the solutions to a…
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.
In this paper, persistence of solitary wave solutions of the regularized long wave equation with small perturbations are investigated by the geometric singular perturbation theory. Two different kinds of the perturbations are considered in…
We study a system of forced viscous shallow water equations with nontrivial bathymetry in two spatial dimensions. We develop a well-posedness theory for small but arbitrary forcing data, as well as for a fixed data profile but large…
We make some remarks on the linear wave equation concerning the existence and uniqueness of weak solutions, satisfaction of the energy equation, growth properties of solutions, the passage from bounded to unbounded domains, and…
We consider a system of stochastic partial differential equations modeling heat conduction in a non-linear medium. We show global existence of solutions for the system in Sobolev spaces of low regularity, including spaces with norm beneath…
The construction of stochastic solutions is a powerful method to obtain localized solutions in configuration or Fourier space and for parallel computation with domain decomposition. Here a stochastic solution is obtained for the…
A recently developed method has been extended to a nonlocal equation arising in steady water wave propagation in two dimensions. We obtain analyic approximation of steady water wave solution in two dimensions with rigorous error bounds for…
In this paper we give a meaning to the nonlinear characteristic Cauchy problem for the Wave Equation in base form by replacing it by a family of non-characteristic problems in an appropriate algebra of generalized functions. We prove…
The quantum mechanics is considered to be a partial case of the stochastic system dynamics. It is shown that the wave function describes the state of statistically averaged system $<\mathcal{S}_{st}>$, but not that of the individual…
The generalized method of characteristics is used to obtain rank-2 solutions of the classical equations of hydrodynamics in (3+1) dimensions describing the motion of a fluid medium in the presence of gravitational and Coriolis forces. We…
In recent times it has been paid attention to the fact that (linear) wave equations admit of "soliton-like" solutions, known as Localized Waves or Non-diffracting Waves, which propagate without distortion in one direction. Such Localized…
We consider the wave equation with highly oscillatory initial data, where there is uncertainty in the wave speed, initial phase and/or initial amplitude. To estimate quantities of interest related to the solution and their statistics, we…
The article explores the acoustic equations in inhomogeneous media and the linearized shallow water equations. Two methods for integrating these equations are proposed. The first method is based on the of the Laplace cascade method, while…