Some Estimates for Spatially Unbounded Solutions of Burgers Equation with Non-Autonomous Forcing

Abstract

In this paper, we consider 1-Dimensional Burgers equation in   with a time-dependent forcing term that may be allowed to grow slightly as the spatial variable grows. We have introduced some family of special weights, given the attendant difficulty of considering a function in the whole space, to gain control of the function. Under a special assumption, it is found that the Burgers equation possess, at least, one solution in the phase space of the weight that satisfies the dissipative estimates. The existence and uniqueness of the solution is also been obtained.