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Related papers: Aperiodic fractional obstacle problems

200 papers

We study variational obstacle avoidance problems on complete Riemannian manifolds and apply the results to the construction of piecewise smooth curves interpolating a set of knot points in systems with impulse effects. We derive the…

Optimization and Control · Mathematics 2021-08-31 Jacob R. Goodman , Leonardo J. Colombo

In cosmology an important role is played by homogeneous and isotropic solutions of the Einstein-Euler equations and linearized perturbations of these. This paper proves results on the asymptotic behaviour of scalar perturbations both in the…

Analysis of PDEs · Mathematics 2009-06-16 Paul T. Allen , Alan D. Rendall

In this article we give a brief overview of some known results in the theory of obstacle-type problems associated with a class of fourth-order elliptic operators, and we highlight our recent work with collaborators in this direction.…

Analysis of PDEs · Mathematics 2024-01-23 Donatella Danielli , Alaa Haj Ali

This paper deals with the existence, monotonicity, uniqueness and asymptotic behaviour of travelling wavefronts for a class of temporally delayed, spatially nonlocal diffusion equations.

Dynamical Systems · Mathematics 2017-03-01 Shangjiang Guo , Johannes Zimmer

Difference schemes for the time-fractional diffusion equation with variable coefficients and nonlocal boundary conditions containing real parameters $\alpha$ and $\beta$ are considered. By the method of energy inequalities, for the solution…

Numerical Analysis · Mathematics 2015-03-27 A. A. Alikhanov

The existence of weak solutions to the obstacle problem for a nonlocal semilinear fourth-order parabolic equation is shown, using its underlying gradient flow structure. The model governs the dynamics of a microelectromechanical system with…

Analysis of PDEs · Mathematics 2019-10-10 Philippe Laurençot , Christoph Walker

We show that the solutions to the nonlocal obstacle problems for the nonlocal $-\Delta_p^s$ operator, when the fractional parameter $s\to\sigma$ for $0<\sigma\leq1$, converge to the solution of the corresponding obstacle problem for…

Analysis of PDEs · Mathematics 2025-05-14 Catharine W. K. Lo , José Francisco Rodrigues

Caputo fractional (with power-law kernels) and fractional (delta) difference maps belong to a more widely defined class of generalized fractional maps, which are discrete convolutions with some power-law-like functions. The conditions of…

Chaotic Dynamics · Physics 2023-03-10 Mark Edelman

We study the obstacle problem related to a wide class of nonlinear integro-differential operators, whose model is the fractional subLaplacian in the Heisenberg group. We prove both the existence and uniqueness of the solution, and that…

Analysis of PDEs · Mathematics 2023-01-12 Mirco Piccinini

We here establish the higher fractional differentiability for solutions to a class of obstacle problems with non-standard growth conditions. We deal with the case in which the solutions to the obstacle problems satisfy a variational…

Analysis of PDEs · Mathematics 2021-09-06 Antonio Giuseppe Grimaldi , Erica Ipocoana

We study small perturbations of the Dirichlet problems for second order elliptic equations that degenerate on the boundary. The limit of the solution, as the perturbation tends to zero, is calculated. The result is based on a certain…

Analysis of PDEs · Mathematics 2021-07-01 Mark Freidlin , Leonid Koralov

We theoretically investigate the behavior of a moving impurity immersed in a sea of fermionic atoms that are confined in a quasi-periodic (bichromatic) optical lattice, within a standard variational approach. We consider both repulsive and…

Quantum Gases · Physics 2016-05-11 Hui Hu , An-Bang Wang , Su Yi , Xia-Ji Liu

We study the higher-order asymptotic development of a nonlocal phase transition energy in bounded domains and with prescribed external boundary conditions. The energy under consideration has fractional order $2s \in (0,1)$ and a first-order…

Analysis of PDEs · Mathematics 2024-10-31 Serena Dipierro , Enrico Valdinoci , Mary Vaughan

We investigate the generation of fractional-period states in continuum periodic systems. As an example, we consider a Bose-Einstein condensate confined in an optical-lattice potential. We show that when the potential is turned on…

Other Condensed Matter · Physics 2009-11-11 H. E. Nistazakis , Mason A. Porter , P. G. Kevrekidis , D. J. Frantzeskakis , A. Nicolin , J. K. Chin

We consider the strongly damped Klein Gordon equation for defocusing nonlinearity and we study the asymptotic behaviour of the energy for periodic solutions. We prove first the exponential decay to zero for zero mean solutions. Then, we…

Analysis of PDEs · Mathematics 2022-05-10 Haidar Mohamad

We prove local higher-order asymptotics for extreme water waves with vorticity near stagnation points. We obtain that the behaviour of solutions and their regularity depend substantially on the vorticity. In particular, we show that extreme…

Analysis of PDEs · Mathematics 2021-03-29 Vladimir Kozlov , Evgeniy Lokharu

We establish asymptotic diffusion limits of the non-classical transport equation derived in [E. W. Larsen, A generalized Boltzmann equation for non-classical particle transport, Joint international topical meeting on mathematics &…

Analysis of PDEs · Mathematics 2016-07-15 Martin Frank , Weiran Sun

Within the frame of a Group Approach to Quantization anomalies arise in a quite natural way. We present in this talk an analysis of the basic obstructions that can be found when we try to translate symmetries of the Newton equations to the…

High Energy Physics - Theory · Physics 2007-05-23 V. Aldaya , M. Calixto , J. Guerrero

This paper is concerned with the variational problem for the elastic energy defined on symmetric graphs under the unilateral constraint. Assuming that the obstacle function satisfies the symmetric cone condition, we prove (i) uniqueness of…

Analysis of PDEs · Mathematics 2022-08-10 Kensuke Yoshizawa

This work is a follow-up to our previous work "A numerical approach related to defect-type theories for some weakly random problems in homogenization" (preprint available on this archive). It extends and complements, both theoretically and…

Analysis of PDEs · Mathematics 2010-05-24 Arnaud Anantharaman , Claude Le Bris