Solutions Illustrating the Decay of Dissipation Layers in Burgers' Nonlinear Diffusion Equation
- 1 October 1967
- journal article
- conference paper
- Published by AIP Publishing in Physics of Fluids
- Vol. 10 (10) , 2113-2119
- https://doi.org/10.1063/1.1762006
Abstract
Two exact viscous and nonsteady solutions of Burgers' nonlinear diffusion equation are derived which show how sawtooth discontinuities or dissipation layers broaden and decay. One solution is in the ``physical space''; the other is a discrete spatial Fourier series. Spectral coefficients of the second solution satisfy (exactly) an infinite set of coupled nonlinear ordinary differential equations. Energetics of the two solutions are briefly discussed.Keywords
This publication has 6 references indexed in Scilit:
- Statistical Initial-Value Problem for Burgers' Model Equation of TurbulencePhysics of Fluids, 1966
- Some New Exact, Viscous, Nonsteady Solutions of Burgers' EquationPhysics of Fluids, 1966
- Dynamics of Nonlinear Stochastic SystemsJournal of Mathematical Physics, 1961
- On a quasi-linear parabolic equation occurring in aerodynamicsQuarterly of Applied Mathematics, 1951
- The partial differential equation ut + uux = μxxCommunications on Pure and Applied Mathematics, 1950
- A Mathematical Model Illustrating the Theory of TurbulencePublished by Elsevier ,1948