23,399 research outputs found
A mixed problem with only integral boundary conditions for a hyperbolic equation
We investigate an initial boundary value problem for a
second-order hyperbolic equation with only integral conditions.
We show the existence, uniqueness, and continuous dependence of a
strongly generalized solution. The proof is based on an energy
inequality established in a nonclassical function space, and on
the density of the range of the operator associated to the
abstract formulation of the studied problem by introducing
special smoothing operators
On the Volterra property of a boundary problem with integral gluing condition for mixed parabolic-hyperbolic equation
In the present work we consider a boundary value problem with gluing
conditions of integral form for parabolic-hyperbolic type equation. We prove
that the considered problem has the Volterra property. The main tools used in
the work are related to the method of the integral equations and functional
analysis.Comment: 18 page
Energy 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
introduced by Lupo, Morawetz, and Payne for a generalized Tricomi operator. The
existence of strong solutions under open boundary conditions is also proven.Comment: 33 page
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