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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2005