Search results for " Nonlinear"
showing 10 items of 1224 documents
Singular (p, q)-equations with superlinear reaction and concave boundary condition
2020
We consider a parametric nonlinear elliptic problem driven by the sum of a p-Laplacian and of a q-Laplacian (a (Formula presented.) -equation) with a singular and (Formula presented.) -superlinear reaction and a Robin boundary condition with (Formula presented.) -sublinear boundary term (Formula presented.). So, the problem has the combined effects of singular, concave and convex terms. We look for positive solutions and prove a bifurcation-type theorem describing the changes in the set of positive solutions as the parameter varies.
Existence of two solutions for singular Φ-Laplacian problems
2022
AbstractExistence of two solutions to a parametric singular quasi-linear elliptic problem is proved. The equation is driven by theΦ\Phi-Laplacian operator, and the reaction term can be nonmonotone. The main tools employed are the local minimum theorem and the Mountain pass theorem, together with the truncation technique. GlobalC1,τ{C}^{1,\tau }regularity of solutions is also investigated, chiefly viaa prioriestimates and perturbation techniques.
On the Stability of the Soft Pendulum With Affine Curvature: Open-Loop, Collocated Closed-Loop, and Switching Control
2022
This letter investigates the stability properties of the soft inverted pendulum with affine curvature - a template model for nonlinear control of underactuated soft robots. We look at how changes in physical parameters affect stability and equilibrium. We give conditions under which zero dynamics corresponding to a collocated choice of the output is (locally or globally) stable or unstable. We leverage these results to design a switching controller that stabilizes a class of nonlinear equilibria of the pendulum, which can drive the system from one equilibrium to another.
Multimode Representation of the Magnetic Field for the Analysis of the Nonlinear Behavior of Solar Activity as a Driver of Space Weather
2022
ISSP UL as the Center of Excellence is supported through the Framework Program for European universities Union Horizon 2020, H2020-WIDESPREAD-01-2016-2017-TeamingPhase2 under Grant Agreement No. 739508, CAMART2 project; Internal Foundation of University of Maryland.
The effect of defect location on coating fragmentation patterns under biaxial tension
2005
Fragmentation of a coating possessing orthogonal preferential crack propagation directions is modeled for equibiaxial tensile loading. Two plausible cracking scenarios are compared, caused by flaws randomly distributed over the area of the coating or along the coating fragment edges. The two fragmentation scenarios considered are shown to yield qualitatively different fragment patterns.
A New Family of Deformations of Darboux-Pöschl-Teller Potentials
2004
The aim of this Letter is to present a new family of integrable functional-difference deformations of the Schrodinger equation with Darboux–Poschl–Teller potentials. The related potentials are labeled by two integers m and n, and also depend on a deformation parameter h. When h→ 0 the classical Darboux–Poschl–Teller model is recovered.
Investigation of Nonlinear Optical Processes in Mercury Sulfide Quantum Dots
2022
European Regional Development Fund (1.1.1.5/19/A/003), State Assignment to Higher Educational Institutions of Russian Federation (FZGU-2020-0035), Russian Foundation for Basic Research (18-29-20062). Institute of Solid State Physics, University of Latvia as the Center of Excellence acknowledges funding from the European Union’s Horizon 2020 Framework Programme H2020-WIDESPREAD-01-2016-2017-TeamingPhase2 under grant agreement No. 739508, project CAMART2.
Nonlinear evolution equations for turbulent superfluids
2010
In this paper a system of evolution equations for turbulent superfluid helium is written in the nonlinear regime, choosing as fundamental fields the density, the velocity, the heat flux, the non-equilibrium temperature and the average vortex line density per unit volume. Approximate equations are written, where second order terms in the non-equilibrium quantities are retained.
Nonlinear black-box models for short-term forecasting of air temperature in the town of Palermo
2011
Weather data are crucial to correctly design buildings and their heating and cooling systems and to assess their energy performances. In the intensely urbanized towns the effect of climatic parameters is further emphasized by the Urban Heat Island (UHI) phenomenon, known as the increase in the air temperature of urban areas, compared to the one measured in the extra-urban areas. The analysis of the heat island needs detailed local climate data which can be collected only by a dedicated weather monitoring system. The Department of Energy and Environmental Researches of the University of Palermo (Italy) has built up a weather monitoring system that works 24 hours per day and makes data availa…
Game-Theoretic Approach to Hölder Regularity for PDEs Involving Eigenvalues of the Hessian
2021
AbstractWe prove a local Hölder estimate for any exponent $0<\delta <\frac {1}{2}$ 0 < δ < 1 2 for solutions of the dynamic programming principle $$ \begin{array}{@{}rcl@{}} u^{\varepsilon} (x) = \sum\limits_{j=1}^{n} \alpha_{j} \underset{\dim(S)=j}{\inf} \underset{|v|=1}{\underset{v\in S}{\sup}} \frac{u^{\varepsilon} (x + \varepsilon v) + u^{\varepsilon} (x - \varepsilon v)}{2} \end{array} $$ u ε ( x ) = ∑ j = 1 n α j inf dim ( S ) = j sup v ∈ S | v | = 1 u ε ( x + ε v ) + u ε ( x − ε v ) 2 with α1,αn > 0 and α2,⋯ ,αn− 1 ≥ 0. The proof is based on a new coupling idea from game theory. As an application, we get the same regularity estimate for viscosity solutions of the PDE $…