Related papers: Nonsmooth Analysis of Doubly Nonlinear Second-Orde…
In this paper, we consider a new kind of evolution multivalued quasi-variational inequalities with feedback effect and a nonlinear bifunction which contain several (evolution) quasi-variational/hemivariational inequalities as special cases.…
Complementing the analysis in [41], we investigate the well-posedness of SPDEs problems of doubly nonlinear type. These arise ubiquitously in the modelization of dissipative media and correspond to generalized balance laws between…
We consider a second order equation with a linear "elastic" part and a nonlinear damping term depending on a power of the norm of the velocity. We investigate the asymptotic behavior of solutions, after rescaling them suitably in order to…
We consider an abstract nonlinear second order evolution equation, inspired by some models for damped oscillations of a beam subject to external loads or magnetic fields, and shaken by a transversal force. When there is no external force,…
This paper presents a variational approach to doubly-nonlinear (gradient) flows (P) of nonconvex energies along with nonpotential perturbations (i.e., perturbation terms without any potential structures). An elliptic-in-time regularization…
This paper is concerned with a parabolic evolution equation of the form $A(u_t) + B(u) = f$, settled in a smooth bounded domain of ${\bf R}^d$, $d \geq 1$, and complemented with the initial conditions and with (for simplicity) homogeneous…
We consider second-order evolution equations in an abstract setting with intermittently delayed/ not-delayed damping. We give sufficient conditions for asymptotic and exponential stability, improving and generalising our previous results…
In this paper we consider second order evolution equations with unbounded dynamic feedbacks. Under a regularity assumption we show that observability properties for the undamped problem imply decay estimates for the damped problem. We…
We consider a class of abstract second order evolution equations with a restoring force that is strictly superlinear at infinity with respect to the position, and a dissipation mechanism that is strictly superlinear at infinity with respect…
In this study, we analyze a semilinear damped evolution equation under different damping conditions, including the undamped $(\theta=0)$, effectively damped $(0<2\theta<\sigma)$, critically damped $(2\theta=\sigma)$, and non-effectively…
In this work, we address a parabolic problem featuring a potentially doubly nonlinear term, governed by a combination of local and nonlocal operators (see Problem P1 below). We first establish the local existence of weak energy solutions…
In this paper we consider second order evolution equations with bounded damping. We give a characterization of a non uniform decay for the damped problem using a kind of observability estimate for the associated undamped problem.
The paper proposes and develops new globally convergent algorithms of the generalized damped Newton type for solving important classes of nonsmooth optimization problems. These algorithms are based on the theory and calculations of…
We study the asymptotic convergence properties, as the time variable goes to infinity, of trajectories of second-order dissipative evolution equations combining potential with non-potential effects. We exhibit a sharp condition, involving…
First, using the uniform decomposition in both physical and frequency spaces, we obtain an equivalent norm on modulation spaces. Secondly, we consider the Cauchy problem for the dissipative evolutionary pseudo-differential equation…
We investigate the regularity of the strongly continuous semigroup associated with a system of two coupled second order evolution equations with indirect damping, whose stability was recently studied by Hao et al. By deriving the asymptotic…
We consider a rather general class of evolutionary PDEs involving dissipation (of possibly fractional order), which competes with quadratic nonlinearities on the regularity of the overall equation. This includes as prototype models,…
We study a class of nonlinear eigenvalue problems which involves a convolution operator as well as a superlinear nonlinearity. Our variational existence proof is based on constrained optimization and provides a one-parameter family of…
In this paper we study well-posedness and asymptotic stability for a class of nonlinear second-order evolution equations with intermittent delay damping. More precisely, a delay feedback and an undelayed one act alternately in time. We show…
In the present paper, we prove time decay estimates of solutions in weighted Sobolev spaces to the second order evolution equation with fractional Laplacian and damping for data in Besov spaces. Our estimates generalize the estimates…