Duke Applied Mathematics

Publications [#244194] of Thomas P. Witelski

Papers Published

1. Witelski, TP, Shocks in nonlinear diffusion, Applied Mathematics Letters, vol. 8 no. 5 (January, 1995), pp. 27-32, Elsevier BV, ISSN 0893-9659 [gz], [doi]
   (last updated on 2024/04/19)

   Abstract:
   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.