Weak and strong solutions to boundary-value problems in the cold plasma model
نویسنده
چکیده
Boundary-value problems are formulated for elliptic-hyperbolic systems that model electromagnetic wave propagation in an idealized plasma. MSC2000 : 35M10, 35D05, 82D10
منابع مشابه
Unique Solutions to Boundary Value Problems in the Cold Plasma Model
The existence of a unique weak solution to the homogeneous closed Dirichlet problem is proven for an elliptic-hyperbolic equation. The equation arises in a model for electromagnetic wave propagation in cold plasma. A class of open boundary value problems for the equation is shown to possess strong solutions. MSC2000 : 35M10, 35D05, 82D10.
متن کاملEnergy Inequalities for a Model of Wave Propagation in Cold Plasma
Energy inequalities are derived for an elliptic-hyperbolic operator arising in plasma physics. These inequalities imply the existence of distribution and weak solutions to various closed boundary-value problems. An existence theorem is proven for a related class of Keldysh equations, and the failure of expected methods for obtaining uniqueness is discussed. The proofs use ideas recently introdu...
متن کاملMathematical aspects of the cold plasma model
A simple model for electromagnetic wave propagation through zerotemperature plasma is analyzed. Many of the complexities of the plasma state are present even under these idealized conditions, and a number of mathematical difficulties emerge. In particular, boundary value problems formulated on the basis of conventional electromagnetic theory turn out to be ill-posed in this context. However, co...
متن کاملOn Approximate Stationary Radial Solutions for a Class of Boundary Value Problems Arising in Epitaxial Growth Theory
In this paper, we consider a non-self-adjoint, singular, nonlinear fourth order boundary value problem which arises in the theory of epitaxial growth. It is possible to reduce the fourth order equation to a singular boundary value problem of second order given by w''-1/r w'=w^2/(2r^2 )+1/2 λ r^2. The problem depends on the parameter λ and admits multiple solutions. Therefore, it is difficult to...
متن کاملExistence of at least three weak solutions for a quasilinear elliptic system
In this paper, applying two theorems of Ricceri and Bonanno, we will establish the existence of three weak solutions for a quasilinear elliptic system. Indeed, we will assign a differentiable nonlinear operator to a differential equation system such that the critical points of this operator are weak solutions of the system. In this paper, applying two theorems of R...
متن کامل