In this work, we consider the forced generalized Burgers-Huxley equation and establish existence uniqueness of a global weak solution using Faedo-Galerkin approximation method. Under smoothness assumptions on initial data external forcing, also obtain further regularity results solutions. Taking forcing to be zero, positivity result as well bound classical are estab...

We consider the Langevin equation describing a non-viscous Burgers fluid stochastically perturbed by uniform noise. We introduce a deterministic function that corresponds to the mean of the velocity when we keep fixed the value of the position. We study interrelations between this function and the solution of the non-perturbed Burgers equation. Especially we are interested in the property of th...

Non-local transformation, which connects the 3-dimensional Burgers-type equation with a linear heat equation, is constructed. Via this transformation, nonlinear superposition formulae for solutions are obtained and the conditional non-local symmetry of this equation is studied. The multidimensional generalization of the Burgers equation L1(u) = u0 − u|∇u| − u = 0, (1) is called further the Burg...

In this work, we construct the general solution to the Heat Equation (HE) and to many tensor structures associated to the Heat Equation, such as Symmetries, Lagrangians, Poisson Brackets (PB) and Lagrange Brackets (LB), using newly devised techniques that may be applied to any linear equation (e.g., Schrödinger Equation in field theory, or the small-oscillations problem in mechanics). In partic...

This paper examines the properties of a regularization of Burgers equation in one and multiple dimensions using a filtered convective velocity, which we have dubbed as convectively filtered Burgers (CFB) equation. A physical motivation behind the filtering technique is presented. An existence and uniqueness theorem for multiple dimensions and a general class of filters is proven. Multiple invar...