Solution of the Burgers equation on semiinfinite and finite intervals via a stream function

摘要

The initial-boundary-value problem on the semiinfinite interval and on a finite interval for the Burgers equation ut = uxx + 2uxu is solved using a stream functionφand a linearizing transformation w = eφ. The transformation reduces the equation to a heat equation with appropriate initial and homogeneous time-dependent linear boundary conditions. One advantage of this method is that we never need to find an explicit expression for φ in our computations.