Asymptotic Regularity and Existence of Time-Dependent Attractors for Second-Order Undamped Evolution Equations with Memory

Asymptotic Stability of Second-order Evolution Equations with Intermittent Delay

We consider second-order evolution equations in an abstract setting with intermittently delayed/not-delayed damping and give sufficient conditions ensuring asymptotic and exponential stability results. Our abstract framework is then applied to the wave equation, the elasticity system, and the Petrovsky system. For the Petrovsky system with clamped boundary conditions, we further prove an intern...

Resonance in Undamped Second-order Nonlinear Equations with Periodic Forcing

where g and p are real valued functions continuous on the reals R , p(t+2n) = p(t), and the solutions of (1) are uniquely determined by their initial conditions. If g is nonlinear, the question of whether all solutions of (1) are bounded on R has long been recognized as nontrivial and challenging. For the special case of g(x) = 2x Morris [1] was able to show that this question has an affirmativ...

Asymptotic Stability for Intermittently Controlled Second-Order Evolution Equations

Motivated by several works on ordinary differential equations, we are interested in the asymptotic stability of intermittently controlled partial differential equations. We give a condition of asymptotic stability for second-order evolution equations uniformly damped by an on/off feedback. This result extends to the case of partial differential equations a previous result of R. A. Smith concern...

Semilinear Evolution Equations of Second Order via Maximal Regularity

Regularity for Quasilinear Second-Order Subelliptic Equations

In this paper, we study the regularity of solutions of the quasilinear equation where X = ( X , ; . . , X , , , ) is a system of real smooth vector fields, A i j , B E Cw(Q x R m + l ) . Assume that X satisfies the Hormander condition and ( A , , ( x , z , c ) ) is positive definite. We prove that if u E S2@(Q) (see Section 2) is a solution of the above equation, then u E Cw(Q). Introduction In...