Dirac Mass Dynamics in Multidimensional Nonlocal Parabolic Equations

From MaRDI portal
Publication:3104545

DOI10.1080/03605302.2010.538784zbMath1229.35113arXiv1011.1768OpenAlexW2949954288WikidataQ60502796 ScholiaQ60502796MaRDI QIDQ3104545

Perthame, Benoît, Sepideh Mirrahimi, Alexander Lorz

Publication date: 14 December 2011

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1011.1768




Related Items (73)

Dirac concentrations in a chemostat model of adaptive evolutionA Hamilton-Jacobi approach to evolution of dispersalOn a 1D model with nonlocal interactions and mass concentrations: an analytical-numerical approach*Travelling wave solutions of the cubic nonlocal Fisher-KPP equation: I. General theory and the near local limitInvasion fronts and adaptive dynamics in a model for the growth of cell populations with heterogeneous mobilityA class of Hamilton-Jacobi equations with constraint: uniqueness and constructive approachSelection-mutation dynamics with asymmetrical reproduction kernelsMass concentration in a nonlocal model of clonal selectionAsymptotic analysis and optimal control of an integro-differential system modelling healthy and cancer cells exposed to chemotherapyDynamics of concentration in a population model structured by age and a phenotypical traitGlobal existence and asymptotic behavior of solutions to a nonlocal Fisher-KPP type problemAdaptive dynamics of hematopoietic stem cells and their supporting stroma: a model and mathematical analysisAncestral lineages in mutation selection equilibria with moving optimumOn the mathematical theory of post-Darwinian mutations, selection, and evolutionStability of Dirac concentrations in an integro-PDE model for evolution of dispersalWavefronts for a nonlinear nonlocal bistable reaction-diffusion equation in population dynamicsAn unconditionally positivity-preserving implicit-explicit scheme for evolutionary stable distribution modelAn asymptotic preserving scheme for capturing concentrations in age-structured models arising in adaptive dynamicsEvolution of species trait through resource competitionA Hamilton-Jacobi approach for front propagation in kinetic equationsAsymptotic analysis of a selection model with spaceCollective motion driven by nutrient consumptionFilling the gap between individual-based evolutionary models and Hamilton-Jacobi equationsReplicator-mutator equations with quadratic fitnessAsymptotic dynamics in populations structured by sensitivity to global warming and habitat shrinkingAdaptation of a quantitative trait to a changing environment: new analytical insights on the asexual and infinitesimal sexual modelsOn a non-local selection–mutation model with a gradient flow structureOn the Fisher‐KPP model with nonlocal nonlinear sourcesExistence, uniqueness and ergodicity for the centered Fleming-Viot processConcentration in Lotka-Volterra parabolic equations: an asymptotic-preserving schemeSelection-mutation dynamics with spatial dependenceThe Cauchy problem for the infinitesimal model in the regime of small varianceMultiscale eco-evolutionary models: from individuals to populationsGlobal boundedness, hair trigger effect, and pattern formation driven by the parametrization of a nonlocal Fisher-KPP problemUniqueness of the viscosity solution of a constrained Hamilton-Jacobi equationRare Mutations Limit of a Steady State Dispersal Evolution ModelAsymptotic analysis of selection-mutation models in the presence of multiple fitness peaksAdaptation in General Temporally Changing EnvironmentsGlobal stability with selection in integro-differential Lotka-Volterra systems modelling trait-structured populationsUniform boundedness and global existence of solutions to a quasilinear diffusion equation with nonlocal Fisher-KPP type reaction termAn integro-PDE model for evolution of random dispersalLarge time behavior and Lyapunov functionals for a nonlocal differential equationDynamics of adaptation in an anisotropic phenotype-fitness landscapeEvolutionary dynamics of phenotype-structured populations: from individual-level mechanisms to population-level consequencesDirect competition results from strong competition for limited resourceConcentration phenomenon in some non-local equationDirac-concentrations in an integro-PDE model from evolutionary game theoryThe impact of cell density and mutations in a model of multidrug resistance in solid tumorsTime fluctuations in a population model of adaptive dynamicsTravelling Waves in a Nonlocal Reaction-Diffusion Equation as a Model for a Population Structured by a Space Variable and a Phenotypic TraitInvasion fronts with variable motility: phenotype selection, spatial sorting and wave accelerationSurvival criterion for a population subject to selection and mutations; application to temporally piecewise constant environmentsParameter identification in a structured population modelLong Time Evolutionary Dynamics of Phenotypically Structured Populations in Time-Periodic EnvironmentsDynamics of concentration in a population structured by age and a phenotypic trait with mutations. Convergence of the correctorSingular limits for models of selection and mutations with heavy-tailed mutation distributionSpreading in kinetic reaction–transport equations in higher velocity dimensionsAdaptation in a heterogeneous environment I: persistence versus extinctionA nonlocal reaction diffusion equation and its relation with Fujita exponentDissecting the dynamics of epigenetic changes in phenotype-structured populations exposed to fluctuating environmentsTime-asymptotic convergence rates towards discrete steady states of a nonlocal selection-mutation modelAsymptotic analysis of a quantitative genetics model with nonlinear integral operatorModeling the Emergence of Phenotypic Heterogeneity in Vascularized TumorsA probabilistic approach to Dirac concentration in nonlocal models of adaptation with several resourcesA structured population model of clonal selection in acute leukemias with multiple maturation stagesEvolutionary branching via replicator-mutator equationsEntropy Satisfying Schemes for Computing Selection Dynamics in Competitive InteractionsTime-asymptotic convergence rates towards the discrete evolutionary stable distributionOn a model of a population with variable motilityQualitative properties for a pseudo-parabolic equation with nonlocal reaction termUniqueness in a class of Hamilton-Jacobi equations with constraintsModeling the effects of space structure and combination therapies on phenotypic heterogeneity and drug resistance in solid tumorsHamilton-Jacobi approach for dynamic population models



Cites Work


This page was built for publication: Dirac Mass Dynamics in Multidimensional Nonlocal Parabolic Equations