Mild solutions to a measure-valued mass evolution problem with flux boundary conditions

DOI10.1016/j.jde.2015.02.037zbMath1315.35057arXiv1210.4118OpenAlexW2025694681MaRDI QIDQ2343529

Joep H. M. Evers, Adrian Muntean, Sander Cornelis Hille

Publication date: 6 May 2015

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1210.4118

zbMATH Keywords

flux boundary conditionconvergence ratemild solutionssingular limitboundary layer asymptoticslinear transport equationsmeasure-valued equationslinear discontinuous production term

Mathematics Subject Classification ID

Spaces of measures (46E27) Volterra integral equations (45D05) Initial-boundary value problems for linear first-order PDEs (35F16)

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Cites Work

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• Mixed systems: ODEs-balance laws
• Structured populations, cell growth and measure valued balance laws
• Time-evolving measures and macroscopic modeling of pedestrian flow
• Embedding of semigroups of Lipschitz maps into positive linear semigroups on ordered Banach spaces generated by measures
• Rate distributions and survival of the fittest: a formulation on the space of measures
• Continuity of the restriction of \(C_0\)-semigroups to invariant Banach subspaces
• Flux terms and Robin boundary conditions as limit of reactions and potentials concentrating at the boundary
• A nonlinear structured population model: Lipschitz continuity of measure-valued solutions with respect to model ingredients
• Semigroups of linear operators and applications to partial differential equations
• Fortet-Mourier norms associated with some iterated function systems
• Markov operators with a unique invariant measure
• Dynamic boundary conditions as limit of singularly perturbed parabolic problems
• Boundedness, global existence and continuous dependence for nonlinear dynamical systems describing physiologically structured populations
• Measure-valued solutions for a hierarchically size-structured population
• Continuity properties of Markov semigroups and their restrictions to invariant \(L^{1}\)-spaces
• Models of Discrete and Continuous Cell Differentiation in the Framework of Transport Equation
• MODELING CROWD DYNAMICS FROM A COMPLEX SYSTEM VIEWPOINT
• Chemical Kinetics on Surfaces: A Singular Limit of a Reaction‐Diffusion System
• Boundary Homogenization for Periodic Arrays of Absorbers
• Convergence of Baire measures
• Convergence de la répartition empirique vers la répartition théorique
• Analytic semigroups and optimal regularity in parabolic problems