The Burgers Equation: Explicit Solutions of an Initial Boundary Value Problem

Here, on the basis of the results obtained ill [9J, we construct the solution of an initial boundary value problem for t he Burgers equation, OUT method is based on the application of the well known Cole-Hopf t ransformalion which relates t.he nonlinear Burgers equation to the linear heat C{luat.ion. Thus, lhe initial boundary value problem for the Burgers equation we are interested in is trasfOflllcd into an initial bound ary value prohlem for a linear diffu sion eq uation (heat equation). The latter is solved in terms of a series expansion of repeated integrals of error functions. The convergence of t.his se ries is provcd co rres ponding to initi,,1 data which are a nalyt.ic in 11/2. Rcmarkably, the solution here presented can be easily expressed ill terms of the initial cond itions on the boundary.