6533b820fe1ef96bd1279b9f
RESEARCH PRODUCT
Nonlinear Diffusion in Transparent Media
Francesco PetittaSalvador MollLorenzo Giacomellisubject
Dirichlet problemflux-saturated diffusion equationsGeneral Mathematicsneumann problemMathematical analysisparabolic equationsBoundary (topology)waiting time phenomenaClassification of discontinuitiesparabolic equations; dirichlet problem; cauchy problem; neumann problem; entropy solutions; flux-saturated diffusion equations; waiting time phenomena; conservation lawsNonlinear systemMathematics - Analysis of PDEsFOS: MathematicsNeumann boundary conditionInitial value problemcauchy problemUniquenessdirichlet problemconservation lawsEntropy (arrow of time)entropy solutionsAnalysis of PDEs (math.AP)Mathematicsdescription
Abstract We consider a prototypical nonlinear parabolic equation whose flux has three distinguished features: it is nonlinear with respect to both the unknown and its gradient, it is homogeneous, and it depends only on the direction of the gradient. For such equation, we obtain existence and uniqueness of entropy solutions to the Dirichlet problem, the homogeneous Neumann problem, and the Cauchy problem. Qualitative properties of solutions, such as finite speed of propagation and the occurrence of waiting-time phenomena, with sharp bounds, are shown. We also discuss the formation of jump discontinuities both at the boundary of the solutions’ support and in the bulk.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2021-02-04 | International Mathematics Research Notices |