Related papers: Classical Solutions for a Class of Burgers Equatio…
In this work we carry out a complete group classification of Burgers' equations.
Self-similar solutions of the equations for the Burgers hierarchy are presented.
In this paper, we address the problem of existence and uniqueness of a global classical solution to a multidimensional stochastic Burgers equation without gradient-type assumptions on the force or the initial condition. The equation is…
A hierarchy of normalized classes of generalized Burgers equations is studied. The equivalence groupoids of these classes are computed. The equivalence groupoids of classes of linearizable generalized Burgers equations are related to those…
Some classes of the rational, periodic and solitary wave solutions for the Burgers hierarchy are presented. The solutions for this hierarchy are obtained by using the generalized Cole - Hopf transformation.
We prove the existence and uniqueness of a classical solution to a multidimensional non-potential stochastic Burgers equation with H\"older continuous initial data. Our motivation is the adhesion model in the theory of formation of the…
In this paper we study the analytic solutions of Burgers-type nonlinear fractional equations by means of the Invariant Subspace Method. We first study a class of nonlinear equations directly related to the time-fractional Burgers equation.…
We are concerned with the Dirichlet problem for a class of Hessian type equations. Applying some new methods we are able to establish the $C^2$ estimates for an approximating problem under essentially optimal structure conditions. Based on…
The Burgers' equation is a one-dimensional momentum equation for a Newtonian fluid. The Cole-Hopf transformation solves the equation for a given initial and boundary condition. However, in most cases the resulting integral equation can only…
Salas, Gomez and Heranandez [A.Y. Salas S., C.A. Gomez S., J.E.C Hernandez, New abundant solutions for tha Burgers equation, Computers and Mathematics with Applications 58 (2009) 514 -520] presented 70 "new exact solutions" of a…
The classical quadratic formula and some of its lesser known variants for solving the quadratic equation are reviewed. Then, a new formula for the roots of a quadratic polynomial is presented.
We study the class of one-dimensional equations driven by a stochastic measure $\mu$. For $\mu$ we assume only $\sigma$-additivity in probability. This class of equations include the Burgers equation and the heat equation. The existence and…
Analytic solutions for Burgers equations with source terms, possibly stiff, represent an important element to assess numerical schemes. Here we present a procedure, based on the characteristic technique to obtain analytic solutions for…
We introduce a new concepts of weak solution for the conservative stochastic Burgers equation in any dimension. The definition is based on weak solution concepts introduced by various authors in order to make sense of equations which do not…
Lie group method provides an efficient tool to solve nonlinear partial differential equations. This paper suggests a fractional Lie group method for fractional partial differential equations. A time-fractional Burgers equation is used as an…
The topic of this paper are similarity solutions occurring in multi-dimensional Burgers' equation. We present a simple derivation of the symmetries appearing in a family of generalizations of Burgers' equation in $d$-space dimensions. These…
We obtain precise large time asymptotics for the Cauchy problem for Burgers type equations satisfying shock profile condition. The proofs are based on the exact a priori estimates for (local) solutions of these equations and a recent result…
This is a summary of articles based on higher order B-splines methods and the variation of B-spline methods such as Quadratic B-spline Finite Elements Method, Exponential Cubic B-Spline Method Septic B-spline Technique, Quintic B-spline…
This work introduces a pathwise notion of solution for the stochastic Burgers equation, in particular, our approach encompasses the Cole-Hopf solution. The developments are based on regularization arguments from the theory of distributions.
This article is devoted to the study of the existence and uniqueness of mild solution to time- and space-fractional stochastic Burgers equation perturbed by multiplicative white noise. The required results are obtained by stochastic…