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Decay properties of periodic, radially symmetric solutions of Sine‐Gordon‐type equations
Author(s) -
Scarpellini B.
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.1670160504
Subject(s) - mathematics , mathematical analysis , type (biology) , polynomial , nonlinear system , traveling wave , exponential function , exponential decay , sine , exponential type , mathematical physics , physics , geometry , quantum mechanics , ecology , biology
We investigate the radially symmetric, nonlinear wave equationand discuss the asymptotic behaviour as r → ∞ of solutions which are T ‐periodic in time t . It is shown that only two possibilities of decay can arise, namely polynomial like t −½(n−1) and exponential e −bt for some b > 0. Existence results are obtained.