Markov operators: applications to diffusion processes and population dynamics
This note contains a survey of recent results concerning asymptotic properties of Markov operators and semigroups. Some biological and physical applications are given.
Matematica ed Ecologia: un’interazione feconda
Mathematical analysis for the peridynamic nonlocal continuum theory
We develop a functional analytical framework for a linear peridynamic model of a spring network system in any space dimension. Various properties of the peridynamic operators are examined for general micromodulus functions. These properties are utilized to establish the well-posedness of both the stationary peridynamic model and the Cauchy problem of the time dependent peridynamic model. The connections to the classical elastic models are also provided.
Mathematical analysis for the peridynamic nonlocal continuum theory*
We develop a functional analytical framework for a linear peridynamic model of a spring network system in any space dimension. Various properties of the peridynamic operators are examined for general micromodulus functions. These properties are utilized to establish the well-posedness of both the stationary peridynamic model and the Cauchy problem of the time dependent peridynamic model. The connections to the classical elastic models are also provided.
Mathematical and numerical analysis of radiative heat transfer in semi-transparent media
This paper is concerned with mathematical and numerical analysis of the system of radiative integral transfer equations. The existence and uniqueness of solution to the integral system is proved by establishing the boundedness of the radiative integral operators and proving the invertibility of the operator matrix associated with the system. A collocation-boundary element method is developed to discretize the differential-integral system. For the non-convex geometries, an element-subdivision algorithm...
Mathematical Aspects of 't Hooft's Eigenvalue Problem in Two-Dimensional Quantum Chromodynamcis Part III.
Mathematical Aspects of 'T Hooft's Eigenvalue Problem in Two-Dimensional Quantum Chromodynamics. Part I. A variational approach, and nodal properties of the eigenfunctions.
Mathematical modeling of the competition between acquired immunity and cancer
In this paper we propose and analyse a model of the competition between cancer and the acquired immune system. The model is a system of integro-differential bilinear equations. The role of the humoral response is analyzed. The simulations are related to the immunotherapy of tumors with antibodies.
Maximal monotone model with delay term of convolution.
Maximal regularity for a class of integro-differential equations with infinite delay in Banach spaces
We use Fourier multiplier theorems to establish maximal regularity results for a class of integro-differential equations with infinite delay in Banach spaces. Concrete equations of this type arise in viscoelasticity theory. Results are obtained for periodic solutions in the vector-valued Lebesgue and Besov spaces. An application to semilinear equations is considered.
Maximal regularity for abstract parabolic problems with inhomogeneous boundary data in -spaces
Maximal regularity for abstract parabolic problems with inhomogeneous boundary data in -spaces
Several abstract model problems of elliptic and parabolic type with inhomogeneous initial and boundary data are discussed. By means of a variant of the Dore-Venni theorem, real and complex interpolation, and trace theorems, optimal -regularity is shown. By means of this purely operator theoretic approach, classical results on -regularity of the diffusion equation with inhomogeneous Dirichlet or Neumann or Robin condition are recovered. An application to a dynamic boundary value problem with surface...
Maximal regularity for flexible structural systems in Lebesgue spaces.
Maximum Principle and Its Application for the Time-Fractional Diffusion Equations
MSC 2010: 26A33, 33E12, 35B45, 35B50, 35K99, 45K05 Dedicated to Professor Rudolf Gorenflo on the occasion of his 80th anniversaryIn the paper, maximum principle for the generalized time-fractional diffusion equations including the multi-term diffusion equation and the diffusion equation of distributed order is formulated and discussed. In these equations, the time-fractional derivative is defined in the Caputo sense. In contrast to the Riemann-Liouville fractional derivative, the Caputo fractional...
Mellin pseudodifferential operators with slowly varying symbols and singular integrals on Carleson curves with Muckenhoupt weights.
Metastable aggregation within a discrete-time model.
Method of semidiscretization in time for quasilinear integrodifferential equations.
Méthode unitaire d'étude des différentes classes de problémes "bien posés" concernant certains systémes intégro-différentiels non linéaires aux opérateurs polyvibrants et aux autocontroles dans les limites d'integration.
Midpoint collocation for Cauchy singular integral equations.
Mixing and some integro-functional equations.