Displaying similar documents to “Ordinary differential systems describing hysteresis effects and numerical simulations.”

A simple mathematical model of the human liver

Lenka Čelechovská (2004)

Applications of Mathematics

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The parameter estimation problem for a continuous dynamical system is a difficult one. In this paper we study a simple mathematical model of the liver. For the parameter identification we use the observed clinical data obtained by the BSP test. Bellman’s quasilinearization method and its modifications are applied.

The problem of data assimilation for soil water movement

François-Xavier Le Dimet, Victor Petrovich Shutyaev, Jiafeng Wang, Mu Mu (2004)

ESAIM: Control, Optimisation and Calculus of Variations

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The soil water movement model governed by the initial-boundary value problem for a quasilinear 1-D parabolic equation with nonlinear coefficients is considered. The generalized statement of the problem is formulated. The solvability of the problem is proved in a certain class of functional spaces. The data assimilation problem for this model is analysed. The numerical results are presented.

Estimates and computations for melting and solidification problems

James M. Greenberg (2001)

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

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In this paper we focus on melting and solidification processes described by phase-field models and obtain rigorous estimates for such processes. These estimates are derived in Section 2 and guarantee the convergence of solutions to non-constant equilibrium patterns. The most basic results conclude with the inequality (E2.31). The estimates in the remainder of Section 2 illustrate what obtains if the initial data is progressively more regular and may be omitted on first reading. We also...

Numerical approximation of dynamic deformations of a thermoviscoelastic rod against an elastic obstacle

Maria I. M. Copetti (2004)

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

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In this paper we consider a hyperbolic-parabolic problem that models the longitudinal deformations of a thermoviscoelastic rod supported unilaterally by an elastic obstacle. The existence and uniqueness of a strong solution is shown. A finite element approximation is proposed and its convergence is proved. Numerical experiments are reported.