We investigate generalizations of the Burgers and Burgers-Huxley equations. The investigations we offer focus attention mainly on presenting explict analytical solutions by means of relating these generalized equations to relativistic 1 + 1 dimensional systems of scalar fields where topological solutions are known to play a role. Emphasis is given on chiral solutions, that is, on the possibilit...

In this paper we study the generalized Burgers equation ut + (u /2)x = f(t)uxx, where f(t) > 0 for t > 0 . We show the existence and uniqueness of classical solutions to the initial value problem of the generalized Burgers equation with rough initial data belonging to L∞(R), as well it is obtained the decay rates of u in L norm are algebra order for p ∈ [1,∞[.

We consider the generalized Burgers equation with and without a time delay when the boundary conditions are periodic with period 2π. For the generalized Burgers equation without a time delay, that is, ut = νuxx − uux + u+ h(x), 0 < x < 2π, t > 0, u(0, t) = u(2π, t), u(x,0) = u0(x), a Lyapunov function method is used to show boundedness and uniqueness of a steady state solution and global stabil...