Pinning of interfaces by localized dry friction
Copyright policy )Pinning of interfaces by localized dry friction
We consider a model for the evolution of an interface in a heterogeneous environment governed by a parabolic equation. The heterogeneity is introduced as obstacles exerting a localized dry friction. Our main result establishes the emergence of a rate-independent hysteresis for suitable randomly distributed obstacles, i.e., interfaces are pinned by the obstacles until a certain critical applied driving force is exceeded. The treatment of such a model in the context of pinning and depinning requires a comparison principle. We prove this property and hence the existence of viscosity solutions. Moreover, under reasonable assumptions, we show that viscosity solutions are equivalent to weak solutions.
24 pages
viscosity solutions, MOTION, random media, equivalence of weak solutions and viscosity solutions, 101002 Analysis, PROPAGATION, Viscosity solutions to PDEs, Mathematics - Analysis of PDEs, Dynamics of phase boundaries in solids, pinning of interfaces, FOS: Mathematics, Pinning of interfaces, PDEs with randomness, stochastic partial differential equations, FIELD, Weak solutions to PDEs, HYSTERESIS, Hysteresis, Rate-independent dissipation Viscosity solutions Random media Hysteresis Pinning of interfaces Equivalence of weak solutions and viscosity solutions, Problems involving hysteresis in solids, Comparison principles in context of PDEs, PDEs with multivalued right-hand sides, Random media, UNIQUENESS, hysteresis, Viscosity solutions, VISCOSITY SOLUTIONS, rate-independent dissipation, 35Q82, 35B51, 35D30, 35D40, 35R60, 35R70, Rate-independent dissipation, PDEs in connection with mechanics of deformable solids, Equivalence of weak solutions and viscosity solutions, Analysis of PDEs (math.AP)
viscosity solutions, MOTION, random media, equivalence of weak solutions and viscosity solutions, 101002 Analysis, PROPAGATION, Viscosity solutions to PDEs, Mathematics - Analysis of PDEs, Dynamics of phase boundaries in solids, pinning of interfaces, FOS: Mathematics, Pinning of interfaces, PDEs with randomness, stochastic partial differential equations, FIELD, Weak solutions to PDEs, HYSTERESIS, Hysteresis, Rate-independent dissipation Viscosity solutions Random media Hysteresis Pinning of interfaces Equivalence of weak solutions and viscosity solutions, Problems involving hysteresis in solids, Comparison principles in context of PDEs, PDEs with multivalued right-hand sides, Random media, UNIQUENESS, hysteresis, Viscosity solutions, VISCOSITY SOLUTIONS, rate-independent dissipation, 35Q82, 35B51, 35D30, 35D40, 35R60, 35R70, Rate-independent dissipation, PDEs in connection with mechanics of deformable solids, Equivalence of weak solutions and viscosity solutions, Analysis of PDEs (math.AP)
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