Kavanagh, Kathleen Rose. Nonsmooth Nonlinearities in Applications From Hydrology. (Under the direction of C.T. Kelley) This work has two parts; simulation of unsaturated flow and optimization of remediation problems. For the unsaturated flow simulation, we propose an adaptive time stepping scheme based on error control for Richards’ equation, a model for flow in unsaturated porous media. The mo...

Dither signals provide an effective way of compensating for nonlinearities in control systems. The seminal works by Zames and Shneydor and more recently by Mossaheb present rigorous tools for systematic design of dithered systems. Their results rely however on a Lipschitz assumption on the nonlinearity and thus do not cover important applications with discontinuities. This paper presents initia...

In this paper, by using the bifurcation method of dynamical systems, we derive traveling wave solutions nonlinear equation UUτyy − UyUτy + U2Uτ 3Uy = 0. Based on relationship between Novikov and equation, present parametric representations smooth nonsmooth soliton for with cubic nonlinearity. These contain peaked soliton, W-shaped periodic solutions. Our work extends some previous results.

in this paper, using clarke’s generalized directional derivative and di-invexity we introduce new concepts of nonsmooth k-α-di-invex and generalized type i univex functions over cones for a nonsmooth vector optimization problem with cone constraints. we obtain some sufficient optimality conditions and mond-weir type duality results under the foresaid generalized invexity and type i cone-univexi...

In this paper we are interested in regularity results to obstacle problems for shearable nonlinearly elastic rods. We work with the geometrically exact Cosserat theory for planar deformations which describes rods that can suffer not only flexure but also extension and shear and it involves general nonlinear constitutive relations. This is a consistent intrinsically one-dimensional theory which,...

Sequential optimality conditions provide adequate theoretical tools to justify stopping criteria for nonlinear programming solvers. Here, nonsmooth approximate gradient projection and complementary approximate Karush-Kuhn-Tucker conditions are presented. These sequential optimality conditions are satisfied by local minimizers of optimization problems independently of the fulfillment of constrai...

In this paper an approach for the stabilization problem of sandwich nonlinear systems containing a general nonsmooth nonlinearity is presented. The proposed solution is based on variable structure control theory and ensures the robust ultimate boundedness of the system trajectories in a neighborhood of the origin. Theoretical results have been validated by simulation on a mechanical system repr...

It is well-known that the dynamics of the Arnold circle map is phase-locked in regions of the parameter space called Arnold tongues. If the map is invertible, the only possible dynamics is either quasiperiodic motion, or phase-locked behavior with a unique attracting periodic orbit. Under the influence of quasiperiodic forcing the dynamics of the map changes dramatically. Inside the Arnold tong...

We establish the existence of an entire solution for a class of stationary Schrödinger equations with subcritical discontinuous nonlinearity and lower bounded potential that blows-up at infinity. The abstract framework is related to Lebesgue–Sobolev spaces with variable exponent. The proof is based on the critical point theory in the sense of Clarke and we apply Chang’s version of the Mountain ...

We develop an exponentially convergent distributed algorithm to minimize a sum of nonsmooth cost functions with set constraint. The constraint generally leads the nonlinearity in algorithms, and results difficulties derive exponential rate. In this article, we remove consensus constraints by exact penalty method, then propose projected subgradient virtue differential inclusion differentiated pr...