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An Age and Spatially Structured Population Model for Proteus Mirabilis Swarm-Colony Development

Ph. Laurençot, Ch. Walker (2008)

Mathematical Modelling of Natural Phenomena

Proteus mirabilis are bacteria that make strikingly regular spatial-temporal patterns on agar surfaces. In this paper we investigate a mathematical model that has been shown to display these structures when solved numerically. The model consists of an ordinary differential equation coupled with a partial differential equation involving a first-order hyperbolic aging term together with nonlinear degenerate diffusion. The system is shown to admit global weak solutions.

An age-dependent model describing the spread of panleucopenia virus within feline populations

W. E. Fitzgibbon, M. Langlais, J. J. Morgan, D. Pontier, C. Wolf (2003)

Banach Center Publications

Global existence results and long time behavior are provided for a mathematical model describing the propagation of Feline Panleucopenia Virus (FPLV) within a domestic cat population; two transmission modes are involved: a direct one from infective cats to susceptible ones, and an indirect one from the contaminated environment to susceptible cats. A more severe impact of the virus on young cats requires an age-structured model.

An algorithm for hybrid regularizers based image restoration with Poisson noise

Cong Thang Pham, Thi Thu Thao Tran (2021)

Kybernetika

In this paper, a hybrid regularizers model for Poissonian image restoration is introduced. We study existence and uniqueness of minimizer for this model. To solve the resulting minimization problem, we employ the alternating minimization method with rigorous convergence guarantee. Numerical results demonstrate the efficiency and stability of the proposed method for suppressing Poisson noise.

An alternating-direction iteration method for Helmholtz problems

Jim Douglas, Jeffrey L. Hensley, Jean Elizabeth Roberts (1993)

Applications of Mathematics

An alternating-direction iterative procedure is described for a class of Helmholz-like problems. An algorithm for the selection of the iteration parameters is derived; the parameters are complex with some having positive real part and some negative, reflecting the noncoercivity and nonsymmetry of the finite element or finite difference matrix. Examples are presented, with an applications to wave propagation.

An Analog of the Tricomi Problem for a Mixed Type Equation with a Partial Fractional Derivative

Kilbas, Anatoly, Repin, Oleg (2010)

Fractional Calculus and Applied Analysis

Mathematics Subject Classification 2010: 35M10, 35R11, 26A33, 33C05, 33E12, 33C20.The paper deals with an analog of Tricomi boundary value problem for a partial differential equation of mixed type involving a diffusion equation with the Riemann-Liouville partial fractional derivative and a hyperbolic equation with two degenerate lines. By using the properties of the Gauss hypergeometric function and of the generalized fractional integrals and derivatives with such a function in the kernel, the uniqueness...

An analysis of noise propagation in the multiscale simulation of coarse Fokker-Planck equations

Yves Frederix, Giovanni Samaey, Dirk Roose (2011)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We consider multiscale systems for which only a fine-scale model describing the evolution of individuals (atoms, molecules, bacteria, agents) is given, while we are interested in the evolution of the population density on coarse space and time scales. Typically, this evolution is described by a coarse Fokker-Planck equation. In this paper, we consider a numerical procedure to compute the solution of this Fokker-Planck equation directly on the coarse level, based on the estimation of the unknown...

An analysis of noise propagation in the multiscale simulation of coarse Fokker-Planck equations

Yves Frederix, Giovanni Samaey, Dirk Roose (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider multiscale systems for which only a fine-scale model describing the evolution of individuals (atoms, molecules, bacteria, agents) is given, while we are interested in the evolution of the population density on coarse space and time scales. Typically, this evolution is described by a coarse Fokker-Planck equation. In this paper, we consider a numerical procedure to compute the solution of this Fokker-Planck equation directly on the coarse level, based on the estimation of the unknown...

An analysis of quantum Fokker-Planck models: a Wigner function approach.

Anton Arnold, José L. López, Peter A. Markowich, Juan Soler (2004)

Revista Matemática Iberoamericana

The analysis of dissipative transport equations within the framework of open quantum systems with Fokker-Planck-type scattering is carried out from the perspective of a Wigner function approach. In particular, the well-posedness of the self-consistent whole-space problem in 3D is analyzed: existence of solutions, uniqueness and asymptotic behavior in time, where we adopt the viewpoint of mild solutions in this paper. Also, the admissibility of a density matrix formulation in Lindblad form with Fokker-Planck...

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