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The quasineutral limit problem in semiconductors sciences

Ling Hsiao (2004)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

The mathematical analysis on various mathematical models arisen in semiconductor science has attracted a lot of attention in both applied mathematics and semiconductor physics. It is important to understand the relations between the various models which are different kind of nonlinear system of P.D.Es. The emphasis of this paper is on the relation between the drift-diffusion model and the diffusion equation. This is given by a quasineutral limit from the DD model to the diffusion equation.

The radiation condition at infinity for the high-frequency Helmholtz equation with source term: a wave packet approach

François Castella (2004)

Journées Équations aux dérivées partielles

We consider the high-frequency Helmholtz equation with a given source term, and a small absorption parameter α > 0 . The high-frequency (or: semi-classical) parameter is ε > 0 . We let ε and α go to zero simultaneously. We assume that the zero energy is non-trapping for the underlying classical flow. We also assume that the classical trajectories starting from the origin satisfy a transversality condition, a generic assumption.Under these assumptions, we prove that the solution u ε radiates in the outgoing...

The resolution of the Navier-Stokes equations in anisotropic spaces.

Dragos Iftimie (1999)

Revista Matemática Iberoamericana

In this paper we prove global existence and uniqueness for solutions of the 3-dimensional Navier-Stokes equations with small initial data in spaces which are Hδi in the i-th direction, δ1 + δ2 + δ3 = 1/2, -1/2 < δi < 1/2 and in a space which is L2 in the first two directions and B2,11/2 in the third direction, where H and B denote the usual homogeneous Sobolev and Besov spaces.

The role of oscillations in the global wellposedness of the 3-D incompressible anisotropic Navier-Stokes equations

Jean-Yves Chemin, Ping Zhang (2005/2006)

Séminaire Équations aux dérivées partielles

Corresponding to the wellposedness result [2] for the classical 3-D Navier-Stokes equations ( N S ν ) with initial data in the scaling invariant Besov space, ℬ p , ∞ - 1 + 3 p , here we consider a similar problem for the 3-D anisotropic Navier-Stokes equations ( A N S ν ) , where the vertical viscosity is zero. In order to do so, we first introduce the Besov-Sobolev type spaces, ℬ 4 - 1 2 , 1 2 and ℬ 4 - 1 2 , 1 2 ( T ) . Then with initial data in the scaling invariant space ℬ 4 - 1 2 , 1 2 , we prove the global wellposedness for ( A N S ν ) provided the norm of initial data is small enough compared...

The Rothe method and time periodic solutions to the Navier-Stokes equations and equations of magnetohydrodynamics

Dana Lauerová (1990)

Aplikace matematiky

The existence of a periodic solution of a nonlinear equation z ' + A 0 z + B 0 z = F is proved. The theory developed may be used to prove the existence of a periodic solution of the variational formulation of the Navier-Stokes equations or the equations of magnetohydrodynamics. The proof of the main existence theorem is based on Rothe method in combination with the Galerkin method, using the Brouwer fixed point theorem.

The Rothe method for the McKendrick-von Foerster equation

Henryk Leszczyński, Piotr Zwierkowski (2013)

Czechoslovak Mathematical Journal

We present the Rothe method for the McKendrick-von Foerster equation with initial and boundary conditions. This method is well known as an abstract Euler scheme in extensive literature, e.g. K. Rektorys, The Method of Discretization in Time and Partial Differential Equations, Reidel, Dordrecht, 1982. Various Banach spaces are exploited, the most popular being the space of bounded and continuous functions. We prove the boundedness of approximate solutions and stability of the Rothe method in L ∞ and...

The scalar Oseen operator - Δ + ∂ / ∂ x 1 in ℝ 2

Chérif Amrouche, Hamid Bouzit (2008)

Applications of Mathematics

This paper solves the scalar Oseen equation, a linearized form of the Navier-Stokes equation. Because the fundamental solution has anisotropic properties, the problem is set in a Sobolev space with isotropic and anisotropic weights. We establish some existence results and regularities in L p theory.

The sharp-interface approach for fluids with phase change: Riemann problems and ghost fluid techniques

Christian Merkle, Christian Rohde (2007)

ESAIM: Mathematical Modelling and Numerical Analysis


Systems of mixed hyperbolic-elliptic conservation laws can serve as models for the evolution of a liquid-vapor fluid with possible sharp dynamical phase changes. We focus on the equations of ideal hydrodynamics in the isothermal case and introduce a thermodynamically consistent solution of the Riemann problem in one space dimension. This result is the basis for an algorithm of ghost fluid type to solve the sharp-interface model numerically. In particular the approach allows to resolve phase transitions...

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