Page 1 Next

Displaying 1 – 20 of 128

Showing per page

A Multiscale Model Reduction Method for Partial Differential Equations

Maolin Ci, Thomas Y. Hou, Zuoqiang Shi (2014)

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

We propose a multiscale model reduction method for partial differential equations. The main purpose of this method is to derive an effective equation for multiscale problems without scale separation. An essential ingredient of our method is to decompose the harmonic coordinates into a smooth part and a highly oscillatory part so that the smooth part is invertible and the highly oscillatory part is small. Such a decomposition plays a key role in our construction of the effective equation. We show...

Analytical approximation of the transition density in a local volatility model

Stefano Pagliarani, Andrea Pascucci (2012)

Open Mathematics

We present a simplified approach to the analytical approximation of the transition density related to a general local volatility model. The methodology is sufficiently flexible to be extended to time-dependent coefficients, multi-dimensional stochastic volatility models, degenerate parabolic PDEs related to Asian options and also to include jumps.

Approximate controllability of linear parabolic equations in perforated domains

Patrizia Donato, Aïssam Nabil (2001)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we consider an approximate controllability problem for linear parabolic equations with rapidly oscillating coefficients in a periodically perforated domain. The holes are ε -periodic and of size ε . We show that, as ε 0 , the approximate control and the corresponding solution converge respectively to the approximate control and to the solution of the homogenized problem. In the limit problem, the approximation of the final state is alterated by a constant which depends on the proportion...

Approximate Controllability of linear parabolic equations in perforated domains

Patrizia Donato, Aïssam Nabil (2010)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we consider an approximate controllability problem for linear parabolic equations with rapidly oscillating coefficients in a periodically perforated domain. The holes are ε-periodic and of size ε. We show that, as ε → 0, the approximate control and the corresponding solution converge respectively to the approximate control and to the solution of the homogenized problem. In the limit problem, the approximation of the final state is alterated by a constant which depends on the proportion...

Asymptotic Behavior of the Solution of the Distribution Diffusion Equation for FENE Dumbbell Polymer Model

I. S. Ciuperca, L. I. Palade (2011)

Mathematical Modelling of Natural Phenomena

This paper deals with the evolution Fokker-Planck-Smoluchowski configurational probability diffusion equation for the FENE dumbbell model in dilute polymer solutions. We prove the exponential convergence in time of the solution of this equation to a corresponding steady-state solution, for arbitrary velocity gradients.

Asymptotic behaviour of a class of degenerate elliptic-parabolic operators: a unitary approach

Fabio Paronetto (2007)

ESAIM: Control, Optimisation and Calculus of Variations

We study the asymptotic behaviour of a sequence of strongly degenerate parabolic equations t ( r h u ) - div ( a h · D u ) with r h ( x , t ) 0 , r h L ( Ω × ( 0 , T ) ) . The main problem is the lack of compactness, by-passed via a regularity result. As particular cases, we obtain G-convergence for elliptic operators ( r h 0 ) , G-convergence for parabolic operators ( r h 1 ) , singular perturbations of an elliptic operator ( a h a and r h r , possibly r 0 ) .

Currently displaying 1 – 20 of 128

Page 1 Next