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Radially symmetric global classical solutions of non‐linear wave equations
Author(s) -
Pecher Hartmut
Publication year - 1993
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.1670160206
Subject(s) - mathematics , bounded function , integer (computer science) , mathematical analysis , order (exchange) , space (punctuation) , wave equation , initial value problem , mathematical physics , linguistics , philosophy , finance , computer science , economics , programming language
The Cauchy problem for semilinear wave equations u tt − Δ u + h (| x |) u p = 0 with radially symmetric smooth ‘large’ data has a unique global classical solution in arbitrary space dimensions if h is non‐negative and p any odd integer provided the smooth factor h vanishes with sufficiently high order at the origin and is bounded together with its derivatives.