A remark on nonlocal Neumann conditions for the fractional Laplacian [PDF]
Archiv der Mathematik, 2020 AbstractWe show how nonlocal boundary conditions of Robin type can be encoded in the pointwise expression of the fractional operator. Notably, the fractional Laplacian of functions satisfying homogeneous nonlocal Neumann conditions can be expressed as a regional operator with a kernel having logarithmic behaviour at the boundary.
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A Quasilinear Parabolic System with Nonlocal Boundary Condition [PDF]
Boundary Value Problems, 2011 We investigate the blow-up properties of the positive solutions to a quasilinear parabolic system with nonlocal boundary condition. We first give the criteria for finite time blowup or global existence, which shows the important influence of nonlocal boundary. And then we establish the precise blow-up rate estimate.
Botao Chen +3 more
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Green functions for stationary problems with nonlocal boundary conditions
Lietuvos Matematikos Rinkinys, 2008 In this paper the Green functions for various stationary problems with nonlocal boundary conditions are investigated.We compare Green functions properties for classical boundary conditions with properties of Green functions for problems with nonlocal ...
Svetlana Roman, Artūras Štikonas
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Mathematics, 2021 It is well known that Stochastic equations had many useful applications in describing numerous events and problems of real world, and the nonlocal integral condition is important in physics, finance and engineering.
Ahmed M. A. El-Sayed, Hoda A. Fouad
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Solitons in Nonlinear Media with an Infinite Range of Nonlocality: First Observation of Coherent Elliptic Solitons and of Vortex-Ring Solitons [PDF]
, 2005 We present an experimental study on wave propagation in highly nonlocal optically nonlinear media, for which far-away boundary conditions significantly affect the evolution of localized beams.
Carmon, Tal +4 more
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Effect of boundary conditions and constitutive relations on the free vibration of nonlocal beams
Results in Physics, 2020 The free vibrations of nonlocal Euler and Timoshenko beams have been studied extensively, but there still remain some problems concerning boundary conditions and constitutive relations.
Gen Li +3 more
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Blow-up for a parabolic system with nonlocal sources and nonlocal boundary conditions [PDF]
Boundary Value Problems, 2015 This paper deals with blow-up properties of solutions to a nonlocal parabolic system with nonlocal boundary conditions. The global existence and finite time blow-up criteria are obtained. Moreover, for some special cases, we establish the precise blow-up rate estimates.
Lixin Tian +3 more
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A nonlocal eigenvalue problem and the stability of spikes for reaction-diffusion systems with fractional reaction rates [PDF]
, 2003 We consider a nonlocal eigenvalue problem which arises in the study of stability of spike solutions for reaction-diffusion systems with fractional reaction rates such as the Sel'kov model, the Gray-Scott system, the hypercycle Eigen and Schuster ...
Dancer E. N. +11 more
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Identification hyperbolic problems with nonlocal conditions
AIP Conference Proceedings, 2018 In the present study, a identification problem with nonlocal conditions for a one-dimensional hyperbolic equation is investigated. Stability estimates for the solution of the identification problem are established. Furthermore, a first order of accuracy difference scheme for the numerical solution of the identification hyperbolic equations problems ...
Ashyralyev A., Emharab F.
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Distributed optimal control of a nonstandard nonlocal phase field system [PDF]
, 2016 We investigate a distributed optimal control problem for a nonlocal phase field model of viscous Cahn-Hilliard type. The model constitutes a nonlocal version of a model for two-species phase segregation on an atomic lattice under the presence of ...
Colli, Pierluigi +2 more
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