Segregation effects and gap formation in cross-diffusion models
Martin Burger, José A. Carrillo, Jan‐Frederik Pietschmann, Markus Schmidtchen
2020Interfaces and Free Boundaries Mathematical Analysis Computation and Applications18 citationsDOI
Abstract
In this paper, we extend the results of [8] by proving exponential asymptotic H^1 -convergence of solutions to a one-dimensional singular heat equation with L^2 -source term that describe evolution of viscous thin liquid sheets while considered in the Lagrange coordinates. Furthermore, we extend this asymptotic convergence result to the case of a time inhomogeneous source. This study has also independent interest for the porous medium equation theory.
Topics & Concepts
Convergence (economics)Heat equationExponential functionDiffusionDiffusion equationMathematicsPorous mediumMathematical analysisApplied mathematicsPhysicsPorosityThermodynamicsMaterials scienceEconomyService (business)Economic growthComposite materialEconomicsNonlinear Partial Differential EquationsAdvanced Mathematical Modeling in EngineeringDifferential Equations and Numerical Methods