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Asymptotic behaviour of solutions to semilinear wave equations with initial data of slow decay
Author(s) -
Kubo Hideo
Publication year - 1994
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.1670171205
Subject(s) - mathematics , initial value problem , homogeneous , wave equation , space (punctuation) , representation (politics) , mathematical analysis , property (philosophy) , cauchy problem , combinatorics , law , philosophy , linguistics , epistemology , politics , political science
Some useful and remarkable property are derived from a representation formula of a radially symmetric solution to the Cauchy problem for a homogeneous wave equation in odd space dimensions. These properties provide us with enough information to consider the semilinear case, namely, the associated integral equation with the problem will be considered on a weighted L∞‐space. This formulation enables us to deal with the problem for slowly decaying initial data.