Local asymptotics for nonlocal convective Cahn-Hilliard equations with W1,1 kernel and singular potential
Elisa Davoli, Luca Scarpa, Lara Trussardi
2021Virtual Community of Pathological Anatomy (University of Castilla La Mancha)33 citationsDOIOpen Access PDF
Abstract
We prove existence of solutions and study the nonlocal-to-local asymptotics for nonlocal, convective, Cahn-Hilliard equations in the case of a W1,1 convolution kernel and under homogeneous Neumann conditions. Any type of potential, possibly also of double-obstacle or logarithmic type, is included. Additionally, we highlight variants and extensions to the setting of periodic boundary conditions and viscosity contributions, as well as connections with the general theory of evolutionary convergence of gradient flows.
Topics & Concepts
MathematicsCahn–Hilliard equationKernel (algebra)Neumann boundary conditionMathematical analysisLogarithmConvergence (economics)HomogeneousBoundary (topology)Type (biology)ConvectionBoundary value problemPartial differential equationPure mathematicsPhysicsMechanicsEconomic growthBiologyCombinatoricsEconomicsEcologySolidification and crystal growth phenomenaAdvanced Mathematical Modeling in EngineeringNonlinear Partial Differential Equations