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10 papers · 2 filters
Cahn-Hilliard equation with dynamic boundary conditions and mass constraint on the boundary
Pierluigi Colli, Takeshi Fukao
The well-known Cahn-Hilliard equation entails mass conservation if a suitable boundary condition is prescribed. In the case when the equation is also coupled with a dynamic boundar…
A doubly nonlinear evolution problem related to a model for microwave heating
Luca Scarpa
This paper is concerned with the existence and uniqueness of the solution to a doubly nonlinear parabolic problem which arises directly from a circuit model of microwave heating. B…
Convergence of interaction-driven evolutions of dislocations with Wasserstein dissipation and slip-plane confinement
Maria Giovanna Mora, Mark Peletier, Lucia Scardia
We consider systems of parallel edge dislocations in a single slip system, represented by points in a two-dimensional domain; the elastic medium is modelled as a continuum. We…
Balanced-Viscosity solutions for multi-rate systems
Alexander Mielke, Riccarda Rossi, Giuseppe Savaré
Several mechanical systems are modeled by the static momentum balance for the displacement coupled with a rate-independent flow rule for some internal variable . We consider…
Best matching Barenblatt profiles are delayed
Jean Dolbeault, Giuseppe Toscani
The growth of the second moments of the solutions of fast diffusion equations is asymptotically governed by the behavior of self-similar solutions. However, at next order, there is…
A boundary control problem for the viscous Cahn-Hilliard equation with dynamic boundary conditions
Pierluigi Colli, Gianni Gilardi, Jürgen Sprekels
A boundary control problem for the viscous Cahn-Hilliard equations with possibly singular potentials and dynamic boundary conditions is studied and first order necessary conditions…