0000000000338343

AUTHOR

Giuseppe Maria Coclite

showing 4 related works from this author

A PDE model for the spatial dynamics of a voles population structured in age

2020

Abstract We prove existence and stability of entropy weak solutions for a macroscopic PDE model for the spatial dynamics of a population of voles structured in age. The model consists of a scalar PDE depending on time, t , age, a , and space x = ( x 1 , x 2 ) , supplemented with a non-local boundary condition at a = 0 . The flux is linear with constant coefficient in the age direction but contains a non-local term in the space directions. Also, the equation contains a term of second order in the space variables only. Existence of solutions is established by compensated compactness, see Panov (2009), and we prove stability by a doubling of variables type argument.

Parabolic–hyperbolic equationEnergy estimateseducation.field_of_studyConstant coefficientsDoubling of variablesPopulation dynamics structured in age and spaceApplied Mathematics010102 general mathematicsPopulationMathematical analysis01 natural sciences010101 applied mathematicsCompact spaceNon-local fluxCompensated compactnessPopulation dynamics structured in age and space Parabolic–hyperbolic equation Non-local flux Boundary value problem Energy estimates Compensated compactness Doubling of variablesBoundary value problem0101 mathematicseducationBoundary value problemAnalysisMathematics
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Analytic solutions and Singularity formation for the Peakon b--Family equations

2012

This paper deals with the well-posedness of the b-family equation in analytic function spaces. Using the Abstract Cauchy-Kowalewski theorem we prove that the b-family equation admits, locally in time, a unique analytic solution. Moreover, if the initial data is real analytic and it belongs to H s with s>3/2, and the momentum density u 0-u 0, xx does not change sign, we prove that the solution stays analytic globally in time, for b≥1. Using pseudospectral numerical methods, we study, also, the singularity formation for the b-family equations with the singularity tracking method. This method allows us to follow the process of the singularity formation in the complex plane as the singularity a…

PhysicsAbstract Cauchy-Kowalewski theoremApplied MathematicsNumerical analysisComplex singularitiesNumerical Analysis (math.NA)Spectral analysisFourier spectrumRate of decayPeakonAnalytic solutionMomentumSingularityMathematics - Analysis of PDEsb-family equationFOS: MathematicsSpectral analysis Complex singularities b-family equation Analytic solution Abstract Cauchy-Kowalewski theoremMathematics - Numerical AnalysisComplex planeSettore MAT/07 - Fisica MatematicaMathematical physicsSign (mathematics)Analysis of PDEs (math.AP)
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AN HYPERBOLIC-PARABOLIC PREDATOR-PREY MODEL INVOLVING A VOLE POPULATION STRUCTURED IN AGE

2020

Abstract We prove existence and stability of entropy solutions for a predator-prey system consisting of an hyperbolic equation for predators and a parabolic-hyperbolic equation for preys. The preys' equation, which represents the evolution of a population of voles as in [2] , depends on time, t, age, a, and on a 2-dimensional space variable x, and it is supplemented by a nonlocal boundary condition at a = 0 . The drift term in the predators' equation depends nonlocally on the density of preys and the two equations are also coupled via classical source terms of Lotka-Volterra type, as in [4] . We establish existence of solutions by applying the vanishing viscosity method, and we prove stabil…

Population dynamicsPopulationType (model theory)Space (mathematics)01 natural sciencesStability (probability)Predator-prey systemsNonlinear Sciences::Adaptation and Self-Organizing SystemsApplied mathematicsQuantitative Biology::Populations and Evolution[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]0101 mathematicseducationEntropy (arrow of time)Variable (mathematics)Mathematicseducation.field_of_studyApplied Mathematics010102 general mathematicsNonlocal boundary value problemNonlocal conservation lawsParabolic-hyperbolic equationsTerm (time)010101 applied mathematicsPopulation dynamics Predator-prey systems Parabolic-hyperbolic equations Nonlocal conservation laws Nonlocal boundary value problemHyperbolic partial differential equationAnalysis
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Up-wind difference approximation and singularity formation for a slow erosion model

2020

We consider a model for a granular flow in the slow erosion limit introduced in [31]. We propose an up-wind numerical scheme for this problem and show that the approximate solutions generated by the scheme converge to the unique entropy solution. Numerical examples are also presented showing the reliability of the scheme. We study also the finite time singularity formation for the model with the singularity tracking method, and we characterize the singularities as shocks in the solution.

granular flowsNumerical AnalysisEntropy solutionsup-wind schemeApplied MathematicsMathematical analysisEngquist–Osher schemeEntropy solutions up-wind scheme Engquist–Osher scheme spectral analysis complex singularities granular flowsspectral analysiscomplex singularitiesComputational MathematicsSingularityEntropy solutions / up-wind scheme / Engquist–Osher scheme / spectral analysis / complex singularities / granular flowsModeling and SimulationSpectral analysisGravitational singularityFinite timeSettore MAT/07 - Fisica MatematicaAnalysisMathematics
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