Abstract
Here, on the basis of the results obtained in [9], we construct the solution of an initial boundary value problem for the Burgers equation.
Our method is based on the application of the well known Cole-Hopf transformation which relates the nonlinear Burgers equation to the linear heat equation. Thus, the initial boundary value problem for the Burgers equation we are interested in is trasformed into an initial boundary value problem for a linear diffusion equation (heat equation).
The latter is solved in terms of a series expansion of repeated integrals of error functions. The convergence of this series is proved corresponding to initial data which are analytic in t 1/2.
Remarkably, the solution here presented can be easily expressed in terms of the initial conditions on the boundary.
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© 1993 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden
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Carillo, S. (1993). The Burgers Equation: Explicit Solutions of an Initial Boundary Value Problem. In: Donato, A., Oliveri, F. (eds) Nonlinear Hyperbolic Problems: Theoretical, Applied, and Computational Aspects. Notes on Numerical Fluid Mechanics (NNFM), vol 43. Vieweg+Teubner Verlag. https://doi.org/10.1007/978-3-322-87871-7_14
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DOI: https://doi.org/10.1007/978-3-322-87871-7_14
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