Shocks in nonlinear diffusion
Using two models that incorporate a nonlinear forward-backward heat equation, we demonstrate the existence of well-defined weak solutions containing shocks for diffusive problems. Occurrence of shocks is connected to multivalued inverse solutions and nonmonotone potential functions. Unique viscous solutions are determined from perturbation theory by matching to a shock layer condition. Results of direct numerical simulations are also discussed. © 1995.
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