Search results for "Mathematical analysis"
showing 10 items of 2409 documents
Analysis of a Parabolic Cross-Diffusion Semiconductor Model with Electron-Hole Scattering
2007
The global-in-time existence of non-negative solutions to a parabolic strongly coupled system with mixed Dirichlet–Neumann boundary conditions is shown. The system describes the time evolution of the electron and hole densities in a semiconductor when electron-hole scattering is taken into account. The parabolic equations are coupled to the Poisson equation for the electrostatic potential. Written in the quasi-Fermi potential variables, the diffusion matrix of the parabolic system contains strong cross-diffusion terms and is only positive semi-definite such that the problem is formally of degenerate type. The existence proof is based on the study of a fully discretized version of the system…
A PDE model for the spatial dynamics of a voles population structured in age
2020
Abstract We prove existence and stability of entropy weak solutions for a macroscopic PDE model for the spatial dynamics of a population of voles structured in age. The model consists of a scalar PDE depending on time, t , age, a , and space x = ( x 1 , x 2 ) , supplemented with a non-local boundary condition at a = 0 . The flux is linear with constant coefficient in the age direction but contains a non-local term in the space directions. Also, the equation contains a term of second order in the space variables only. Existence of solutions is established by compensated compactness, see Panov (2009), and we prove stability by a doubling of variables type argument.
Drawing and extruding: Theoretical and approximate formulas
1969
The problem of drawing of wires and of strips has been treated in several studies; among these the studies of Sachs seem essential. However, the results deduced according to similar theories are not always in accordance with the experimental results: reduction of area or of thickness are in fact usually smaller than those resulting from the theory. This is in dependance of the fact that Sachs has adopted the Limiting Condition of Yielding by v. Mises, according to which the limit values of stress in traction and compression are equal. More recently other AA. (Alberti, Noto La Diega, Bugini), admitting the Limiting Condition of Yielding by A. (or of the Paraboloid of Revolution) of which we …
Parallel Schwarz methods for convection-dominated semilinear diffusion problems
2002
AbstractParallel two-level Schwarz methods are proposed for the numerical solution of convection-diffusion problems, with the emphasis on convection-dominated problems. Two variants of the methodology are investigated. They differ from each other by the type of boundary conditions (Dirichlet- or Neumann-type) posed on a part of the second-level subdomain interfaces. Convergence properties of the two-level Schwarz methods are experimentally compared with those of a variant of the standard multi-domain Schwarz alternating method. Numerical experiments performed on a distributed memory multiprocessor computer illustrate parallel efficiency of the methods.
On the volume of unit vector fields on spaces of constant sectional curvature
2004
A unit vector field X on a Riemannian manifold determines a submanifold in the unit tangent bundle. The volume of X is the volume of this submanifold for the induced Sasaki metric. It is known that the parallel fields are the trivial minima.
On One Identification Problem in Linear Elasticity
1990
In practice we meet problems, when having the solution of partial differential equation, we want to discover parts in the domain of its definition where the solution has some specific properties. In [1] and [2] the problem of identification of a curve φ, lying inside of Ω such that the flux \(\int{_{\varphi }}\frac{\partial u}{\partial n}ds\) is maximal has been studied, where u is the solution of mixed—boundary value problem for Laplacian operator.
Existence and uniqueness for the Prandtl equations
2001
International audience; Under the hypothesis of analyticity of the data with respect to the tangential variable we prove the existence and uniqueness of the mild solution of Prandtl boundary layer equation. This can be considered an improvement of the results of [8] as we do not require analyticity with respect to the normal variable. (C) 2001 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.
Quasi-linear diffusion equations with gradient terms and L1 data
2004
Abstract In this article we study the following quasi-linear parabolic problem: u t − Δ u+|u| β−2 u| ∇ u| q =|u| α−2 u| ∇ u| p in Ω×]0,T[, u(x,t)=0 on ∂Ω×]0,T[, u(x,0)=u 0 (x) in Ω, where Ω is a bounded open set of R N and T>0. We prove that if α,β>1, 0⩽p u 0 ∈L 1 (Ω) .
Formation of Coherent Structures in Kolmogorov Flow with Stratification and Drag
2014
We study a weakly stratified Kolmogorov flow under the effect of a small linear drag. We perform a linear stability analysis of the basic state. We construct the finite dimensional dynamical system deriving from the truncated Fourier mode approximation. Using the Reynolds number as bifurcation parameter we build the corresponding diagram up to Re=100. We observe the coexistence of three coherent structures.
Singular integrals, analytic capacity and rectifiability
1997
In this survey we study some interplay between classical complex analysis (removable sets for bounded analytic functions), harmonic analysis (singular integrals), and geometric measure theory (rectifiability).