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Wave equations with time‐dependent spatial operators of higher order
Author(s) -
Lesky Peter
Publication year - 1992
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670150702
Subject(s) - mathematics , boundary value problem , order (exchange) , homogeneous , scalar (mathematics) , mathematical analysis , differential operator , dirichlet boundary condition , elliptic operator , function (biology) , mathematical physics , pure mathematics , combinatorics , geometry , finance , evolutionary biology , economics , biology
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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