scholarly journals Note on certain nonlinear evolution equations of second order

1979 ◽  
Vol 55 (5) ◽  
pp. 167-171 ◽  
Author(s):  
Yoshio Yamada
Keyword(s):  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Second Order ◽  
Nonlinear Evolution Equations

scholarly journals Optimal control of nonlinear second order evolution equations

1993 ◽  
Vol 6 (2) ◽  
pp. 123-135 ◽  
Author(s):  
N. U. Ahmed ◽  
Sebti Kerbal
Keyword(s):  
Optimal Control ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Second Order ◽  
Nonlinear Evolution Equations ◽  
Optimal Solutions ◽  
Existence Of Optimal Solutions ◽  
Lagrange Problem

In this paper we study the optimal control of systems governed by second order nonlinear evolution equations. We establish the existence of optimal solutions for Lagrange problem.

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

1979 ◽  
Vol 73 ◽  
pp. 69-98 ◽  
Author(s):  
Yoshio Yamada
Keyword(s):  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Second Order ◽  
Nonlinear Evolution Equations ◽  
Nonlinear Operators ◽  
Decay Of Solutions ◽  
Vibrating Membrane

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.

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