On the linear force-free fields in bounded and unbounded three-dimensional domains
On the linear force-free fields in bounded and unbounded three-dimensional domains
Linear Force-free (or Beltrami) fields are three-components divergence-free fields solutions of the equation curlB = αB, where α is a real number. Such fields appear in many branches of physics like astrophysics, fluid mechanics, electromagnetics and plasma physics. In this paper, we deal with some related boundary value problems in multiply-connected bounded domains, in half-cylindrical domains and in exterior domains.
On the mixed problem for quasilinear partial functional differential equations with unbounded delay
We consider the mixed problem for the quasilinear partial functional differential equation with unbounded delay , where is defined by , , and the phase space satisfies suitable axioms. Using the method of bicharacteristics and the fixed-point method we prove a theorem on the local existence and uniqueness of Carathéodory solutions of the mixed problem.
On the numerical approximation of first-order Hamilton-Jacobi equations
Some methods for the numerical approximation of time-dependent and steady first-order Hamilton-Jacobi equations are reviewed. Most of the discussion focuses on conformal triangular-type meshes, but we show how to extend this to the most general meshes. We review some first-order monotone schemes and also high-order ones specially dedicated to steady problems.
On the positivity of an invariant measure on open non-empty sets
On the propagation of singularities of semi-convex functions
On the pullback equation
On the solution of transonic flows with weak shocks
On the solvability of the equation div in and in
We show that the equation div has, in general, no Lipschitz (respectively ) solution if is (respectively ).
On the uniqueness of initial-value problems for partial differential equations of the first order
On the uniqueness of viscosity solutions for first order partial differential-functional equations
We consider viscosity solutions for first order differential-functional equations. Uniqueness theorems for initial, mixed, and boundary value problems are presented. Our theorems include some results for generalized ("almost everywhere") solutions.
On two-dimensional hamiltonian transport equations with Llocp coefficients
Ondes de raréfaction pour des systèmes quasilinéaires hyperboliques multidimensionnels
Ondes semi-linéaires conormales classiques par rapport à deux hypersurfaces transverses
Operational WKB solution to the initial/final-value problem for Beechem-Haas equations.
Optimal Proliferation Rate in a Cell Division Model
We consider a size structured cell population model where a mother cell gives birth to two daughter cells. We know that the asymptotic behavior of the density of cells is given by the solution to an eigenproblem. The eigenvector gives the asymptotic shape and the eigenvalue gives the exponential growth rate and so the Maltusian parameter. The Maltusian parameter depends on the division rule for the mother cell, i.e., symmetric (the two daughter cells have the same size) or asymmetric. We use a...
Oscillations fortes sur un champ linéairement dégénéré