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Levi Conditions and Global Gevrey Regularity for the Solutions of Quasilinear Weakly Hyperbolic Equations
Author(s) -
Reissig Michael,
Yagdjian Karen
Publication year - 1996
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/mana.19961780114
Subject(s) - mathematics , degeneracy (biology) , hyperbolic partial differential equation , initial value problem , pure mathematics , mathematical analysis , cauchy problem , cone (formal languages) , partial differential equation , bioinformatics , algorithm , biology
In the present paper the authors prove a global Gevrey regularity result for the solutions of the Cauchy problem for the quasilinear weakly hyperbolic equation with spatial degeneracy u tt −( a ( x, t ) u x ) x = f ( x, t, u, u x ). The basic tool is a well ‐ posedness result (local existence and cone of dependence) in Gevrey spaces. Such a result can be proved only under the assumption of Levi conditions. Suitable energy estimates lead to the regularity of solutions. This result generalizes results from the strictly hyperbolic case.