arXiv subjects

Maciej Szczeciński

Publications and source records attributed to Maciej Szczeciński.

5 recordsLinked to original sources

arXiv2021

Martingale solution of stochastic hybrid Korteweg - de Vries - Burgers equation

In the paper, we consider a stochastic hybrid Korteweg - de Vries - Burgers type equation with multiplicative noise in the form of cylindrical Wiener process. We prove the existence of a martingale solution to the equation studied. The proof of the existence of the solution is based on two approximations of the considered problem and the compactness method. First, we introduce an auxiliary problem corresponding to the equation studied. Then, we prove the existence of a martingale solution to this problem. Finally, we show that the solution of the auxiliary problem converges, in some sense, to the solution of the equation under consideration.

math.PR↗

arXiv2018

Martingale solution to stochastic extended Korteweg - de Vries equation

We study a stochastic extended Korteweg - de Vries equation driven by a multiplicative noise. We prove the existence of a martingale solution to the equation studied. The proof of the solution is based on two approximations of the problem considered and the compactness method.

math.PR↗

arXiv2018

Martingale solution to stochastic Korteweg - de Vries equation driven by Lévy noise

We study stochastic Korteweg - de Vries equation driven by Lévy noise consisting of the compensated time homogeneous Poisson random measure and a cylindrical Wiener process. We prove the existence of a martingale solution to the equation studied. In proof of the existence theorem we use the Galerkin approximation and several auxiliary results suitable for the problem considered.

math.PR↗

arXiv2017

Existence of mild solution to stochastic extended Korteweg - de Vries equation

In the paper we consider stochastic Korteweg - de Vries - type equation. We give sufficient conditions for the existence and uniqueness of local mild solution to the equation with additive noise. We discuss possibility of globalization of mild solution, as well.

math.AP↗

arXiv2016

Finite element method for extended KdV equations

The finite element method (FEM) is applied to obtain numerical solutions to a recently derived nonlinear equation for the shallow water wave problem. A weak formulation and the Petrov-Galerkin method are used. It is shown that the FEM gives a reasonable description of the wave dynamics of soliton waves governed by extended KdV equations. Some new results for several cases of bottom shapes are presented. The numerical scheme presented here is suitable for taking into account stochastic effects, which will be discussed in a subsequent paper.

physics.flu-dyn↗