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On the decay of solutions for some nonlinear evolution equations of second order

Published online by Cambridge University Press:  22 January 2016

Yoshio Yamada
Yoshio Yamada*
Affiliation:
Department of Mathematics, Faculty of Science, Nagoya University
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In this paper we consider nonlinear evolution equations of the form

(E) u″(t) + Au(t) + B(t)u′(t) = f(t), 0 ≦ t < ∞,

(u′(t) = d2u(t)/dt2, u′(t) = du(t)/dt), where A and B(t) are (possibly) nonlinear operators. Various examples of equations of type (E) arise in physics; for instance, if Au = –Δu and B(t)u′ = | u′ | u′, the equation represents a classical vibrating membrane with the resistance proportional to the velocity.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 73 , March 1979 , pp. 69 - 98
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1979

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