A free boundary problem for a nonlinear diffusion–convection equation is considered. The problem is reduced to a nonlinear integral equation in time which is shown to admit a unique solution for small time. An explicit traveling wave solution,corresponding to the shock solution of the Burgers equation, is also obtained, which travels with the same velocity as that of the free boundary.
On a Free Boundary Problem in a Nonlinear Diffusive-Convective System
DE LILLO, Silvana;SALVATORI, Maria Cesarina;
2003
Abstract
A free boundary problem for a nonlinear diffusion–convection equation is considered. The problem is reduced to a nonlinear integral equation in time which is shown to admit a unique solution for small time. An explicit traveling wave solution,corresponding to the shock solution of the Burgers equation, is also obtained, which travels with the same velocity as that of the free boundary.File in questo prodotto:
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