Abstract
We study the mixed initial-boundary value problem for hyperbolic system of second order outside a closed domain. The existence of solutions to this problem is proved and the estimate for the regularity of solutions is given. The application of the existence theorem to elastrodynamics is discussed.
Highlights
This paper is concerned with the exterior problem for hyperbolic system of second order
We assume that aijkl t, x satisfies aijkl t, x eij ekl ≥ α|E|2, α > 0, 1.2 j,k,l 1
Dafermos and Hrusa proved in 3 the local existence of the Dirichlet problem for the hyperbolic system inside a domain by energy method
Summary
This paper is concerned with the exterior problem for hyperbolic system of second order. Consider the following exterior problem for the hyperbolic system of second order:. Ikawa considered in 1 the mixed problem of a hyperbolic equation of second-order. Dafermos and Hrusa proved in 3 the local existence of the Dirichlet problem for the hyperbolic system inside a domain by energy method. We deal with the exterior problem for the second order hyperbolic system.
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