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The Construction of an Evolution System in the Hyperbolic Case and Applications
Author(s) -
Constantin Adrian
Publication year - 2001
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/1522-2616(200104)224:1<49::aid-mana49>3.0.co;2-5
Subject(s) - mathematics , semigroup , differentiable function , cauchy problem , cauchy distribution , type (biology) , series (stratigraphy) , hyperbolic partial differential equation , evolution equation , initial value problem , mathematical analysis , pure mathematics , partial differential equation , ecology , paleontology , biology
We study the Cauchy problem for abstract linear and quasi–linear non–autonomous evolution equations of hyperbolic type using semigroup theory. Under weak differentiability assumptions on the time regularity of the coefficients we prove well–posedness and regularity of a solution. The abstract results are illustrated by their application to a series of equations of mathematical physics.