On the decay of solutions for some nonlinear evolution equations of second order
- 1 March 1979
- journal article
- research article
- Published by Cambridge University Press (CUP) in Nagoya Mathematical Journal
- Vol. 73, 69-98
- https://doi.org/10.1017/s002776300001833x
Abstract
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.Keywords
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