Related papers: Classical Solutions for a Class of Burgers Equatio…
We derive new solutions of the Schr\"odinger equation which describe the motion of particles in the Penning trap. These solutions are direct counterparts of classical orbits. They are obtained by injection of classical trajectories into the…
The paper is a comprehensive study of the existence, uniqueness, blow up and regularity properties of solutions of the Burgers equation with fractional dissipation. We prove existence of the finite time blow up for the power of Laplacian…
In this note we discuss the diffusive, vector-valued Burgers equations in a three-dimensional domain with periodic boundary conditions. We prove that given initial data in $H^{1/2}$ these equations admit a unique global solution that…
Gathering together some existing results, we show that the solutions to the one-dimensional Burgers equation converge for long times towards the stationary solutions to the steady Burgers equation, whose Fourier spectrum is not integrable.…
In this paper we study one dimensional parabolic free boundary value problem with a nonlocal (integro-differential) condition on the free boundary. We establish global existence-uniqueness of classical solutions assuming that the…
In this paper we study an analogue of the classical Riemann-Hilbert problem stated for the classes of difference and $q$-difference systems. The Birkhoff's existence theorem was generalized in this paper.
A special initial condition for (1+1)-dimensional Burgers equation is considered. It allows to obtain new analytical solutions for an arbitrary low viscosity as well as for the inviscid case. The viscous solution is written as a rational…
In this lecture notes we present the equations and the physics involved in the dynamic of incompressible fluids. We present the mathematical techniques needed in order to prove the existence and uniqueness result for the case where we…
We obtain the exact solution for the Burgers equation with a time dependent forcing, which depends linearly on the spatial coordinate. For the case of a stochastic time dependence an exact expression for the joint probability distribution…
The complete group classification problem for the class of (1+1)-dimensional $r$th order general variable-coefficient Burgers-Korteweg-de Vries equations is solved for arbitrary values of $r$ greater than or equal to two. We find the…
The aim of the work is to construct new polynomial systems, which are solutions to certain functional equations which generalize the second-order differential equations satisfied by the so called classical orthogonal polynomial families of…
In this work, we apply the binary Bell polynomial approach to coupled Burgers system. In other words, we investigate possible integrability of referred system. Bilinear form and soliton solutions are obtained, some figures related to these…
In this paper, we investigate new class of sequences related to fully degenerate Bernoulli numbers and polynomials. From those sequences, we derive some formulae for the degenerate Bernoulli and Euler polynomials.
We provide a simple method to recognize classical orthogonal polynomials on lattices defined only by their coefficients of the three term recurrence relation.
We obtain Schauder estimates for a general class of linear integro-differential equations. The estimates are applied to a scalar non-local Burgers equation and complete the global well-posedness results obtained in \cite{ISV}.
The vector Burgers equation is extended to include pressure gradients and gravity. It is shown that within the framework of the Cole-Hopf transformation there are no physical solutions to this problem. This result is important because it…
Solving Burgers' equation always poses challenge to researchers as for small values of viscosity the analytical solution breaks down. Here we propose to compute numerical solution for a class of generalised Burgers' equation described as $$…
The main purpose of this paper is to consider new sandwich pairs and investigate the existence of solution for a new class of fractional differential equations with $p$-Laplacian via variational methods in $\psi$-fractional space…
We find a new class of the Fuchsian equations, which have an algebraic geometric solutions with the parameter belonging to a hyperelliptic curve. Methods of calculating the algebraic genus of the curve, and its branching points, are…
In this article we study a system of eikonal equations. Our aim is to isolate the solutions which minimise the discontinuity set of the gradient.