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Wave equations with time-dependent spatial operators of higher order

✍ Scribed by Peter Lesky Jr

Publisher: John Wiley and Sons
Year: 1992
Tongue: English
Weight: 611 KB
Volume: 15
Category: Article
ISSN: 0170-4214
DOI: 10.1002/mma.1670150702

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✦ Synopsis

Abstract

We study the initial‐boundary value problem for ∂~t~^2^u(t,x)+A(t)u(t,x)+B(t)∂~t~u(t,x)=f(t,x) on [0,T]×Ω(Ω⊂ℝ^n^) with a homogeneous Dirichlet boundary condition; here A(t) denotes a family of uniformly strongly elliptic operators of order 2__m__, B(t) denotes a family of spatial differential operators of order less than or equal to m, and u is a scalar function. We prove the existence of a unique strong solution u. Furthermore, an energy estimate for u is given.

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