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Nonlocal Symmetries and Generation of Solutions for Partial Differential Equations [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2007 Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/
Tychynin, V. +2 more
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Sensitivity of the Solution to Nonsymmetric Differential Matrix Riccati Equation
, 2021 Nonsymmetric differential matrix Riccati equations arise in many problems related to science and engineering. This work is focusing on the sensitivity of the solution to perturbations in the matrix coefficients and the initial condition.
Hached, Mustapha +5 more
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On Bending of Bernoulli-Euler Nanobeams for Nonlocal Composite Materials
Modelling and Simulation in Engineering, 2016 Evaluation of size effects in functionally graded elastic nanobeams is carried out by making recourse to the nonlocal continuum mechanics. The Bernoulli-Euler kinematic assumption and the Eringen nonlocal constitutive law are assumed in the formulation ...
Luciano Feo, Rosa Penna
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Second order systems with nonlinear nonlocal boundary conditions
Electronic Journal of Qualitative Theory of Differential Equations, 2018 This paper is concerned with the second order differential equation with not necessarily linear nonlocal boundary condition. The existence of solutions is obtained using the properties of the Leray–Schauder degree. The results generalize and improve some
Jean Mawhin +2 more
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Existence result for a nonlocal viscous Cahn-Hillard equation with a degenerate mobility
, 2011 We study a diffusion model of phase field type, consisting of a system of two partial differential equations of second order for the particle densities and the viscosity variable, coupled by a nonlocal drift term.
Farshbaf-Shaker, Hassan
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Spike solutions to a nonlocal differential equation
Communications on Pure and Applied Analysis, 2006 In this paper we consider a nonlocal differential equation, which is a limiting equation of one dimensional Gierer-Meinhardt model. We study the existence of spike steady states and their stability. We also construct a single-spike quasi-equilibrium solution and investigate the dynamics of spike-like solutions.
Changfeng Gui, Zhenbu Zhang
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Finite to infinite steady state solutions, bifurcations of an integro-differential equation
, 2011 We consider a bistable integral equation which governs the stationary solutions of a convolution model of solid–solid phase transitions on a circle. We study the bifurcations of the set of the stationary solutions as the diffusion coefficient is varied to ...
Grinfeld, Michael +12 more
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On stochastic solutions of nonlocal random functional integral equations
Arab Journal of Mathematical Sciences, 2019 In this paper, we use Schauder’s fixed point to establish the existence of at least one solution for a functional nonlocal stochastic differential equation under sufficient conditions in the space of all square integrable stochastic processes with a ...
M.M. Elborai, M.I. Youssef
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Hyperbolic differential-difference equations with nonlocal potentials [PDF]
Ufa Mathematical Journal, 2021 Summary: We consider a three-parametric set of solutions for a two-dimensional hyperbolic differential-difference equation in a half-plane containing the sum of a differential operator and shift operators with respect to a spatial variable ranging on the entire real axis (or a differential-difference equation with nonlocal potentials).
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Steady-state solutions of a mass-conserving bistable equation with a saturating flux
, 2012 We consider a mass-conserving bistable equation with a saturating flux on an interval. This is the quasilinear analogue of the Rubinstein–Steinberg equation, suitable for description of order parameter conserving solid–solid phase transitions in the case
Grinfeld, Michael +3 more
core +1 more source