On the coupling of 1D and 3D Diffusion-Reaction Equations: Application to Tissue Pefusion Problems
Publications associées (64)
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In this paper we show that the incompressible Euler equation on the Sobolev space H-s(R-n), s> n/2+1, can be expressed in Lagrangian coordinates as a geodesic equation on an infinite dimensional manifold. Moreover the Christoffel map describing the geodesi ...
Global Science Press2016
In this paper, we prove global weighted Lorentz and Lorentz-Morrey estimates for gradients of solutions to the quasilinear parabolic equations: in a bounded domain , under minimal regularity assumptions on the boundary of domain and on nonlinearity A. Then ...
Springer Heidelberg2015
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We consider the isentropic compressible Euler system in 2 space dimensions with pressure law p () = (2) and we show the existence of classical Riemann data, i.e. pure jump discontinuities across a line, for which there are infinitely many admissible bounde ...
Wiley-Blackwell2015
The modeling of an incompressible fluid through a porous medium requires to deal with two systems of partial differential equations (PDEs) for the two types of media (fluid and porous). A possible way to couple theses two equations is by using the penaliza ...
2015
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We consider the numerical simulation of integrated heart models for the study of the cardiac functioning with particular emphasis on the coupling of the muscle contraction, the fluid dynamics of the left ventricle, and the interaction with the valves. We a ...
CMBE, Zeta Computational Resources Ltd.2015
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A reduced basis Darcy-Stokes finite element heterogeneous multiscale method (RB-DS-FE-HMM) is proposed for the Stokes problem in porous media. The multiscale method is based on the Darcy-Stokes finite element heterogeneous multiscale method (DS-FE-HMM) int ...
MATHICSE2015
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We study the Darcy problem with log-normal permeability, modeling the fluid flow in a heterogeneous porous medium. A perturbation approach is adopted, expanding the solution in Taylor series around the nominal value of the permeability. The resulting recur ...
MATHICSE2014
Let Omega be a bounded domain of R-N (N >= 2). We obtain a necessary and a sufficient condition, expressed in terms of capacities, for the existence of a solution to the porous medium equation with absorption {u(t) - Delta (vertical bar u vertical bar(m-1) ...
Solutes and drugs are transported in the circulatory system by the blood for which absorption processes occur at the arterial walls. The comprehension, modeling, and numerical simulation of these phenomena, both in physiological and pathological conditions ...
2013
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The simulation of the physiological loading situation of arteries with moderate atherosclerotic plaque may provide additional indicators for medical doctors to estimate if the plaque is likely to rupture and if surgical intervention is required. In particu ...
International Center for Numerical Methods in Engineeering (CIMNE)2014
