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Semidiscretization for a nonlocal parabolic problem [PDF]
International Journal of Mathematics and Mathematical Sciences, 2005 A time discretization technique by Euler forward scheme is proposed to deal with a nonlocal parabolic problem. Existence and uniqueness of the approximate solution are proved.
Abderrahmane El Hachimi +1 more
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Young measures in a nonlocal phase transition problem [PDF]
, 1997 A nonlocal variational problem modelling phase transitions is studied in the framework of Young measures. The existence of global minimisers among functions with internal layers on an infinite tube is proved by combining a weak convergence result ...
Winter, M +5 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 ...
Winter, M +3 more
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Existence result for a nonlocal viscous Cahn-Hillard equation with a degenerate mobility [PDF]
, 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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A NONLOCAL VECTOR CALCULUS, NONLOCAL VOLUME-CONSTRAINED PROBLEMS, AND NONLOCAL BALANCE LAWS [PDF]
Mathematical Models and Methods in Applied Sciences, 2013 A vector calculus for nonlocal operators is developed, including the definition of nonlocal divergence, gradient, and curl operators and the derivation of the corresponding adjoint operators. Nonlocal analogs of several theorems and identities of the vector calculus for differential operators are also presented.
Du, Qiang +3 more
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A nonlocal concave-convex problem with nonlocal mixed boundary data [PDF]
, 2018 The aim of this paper is to study a nonlocal equation with mixed Neumann and Dirichlet external conditions. We prove existence, nonexistence and multiplicity of positive energy solutions and analyze the interaction between the concave-convex nonlinearity
Dieb, Abdelrazek +2 more
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Nonclassical Problem for Ultraparabolic Equation in Abstract Spaces
Journal of Function Spaces, 2016 Nonclassical problem for ultraparabolic equation with nonlocal initial condition with respect to one time variable is studied in abstract Hilbert spaces.
Gia Avalishvili, Mariam Avalishvili
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Lietuvos Matematikos Rinkinys, 2021 In this paper, relations between discrete Sturm--Liouville problem with nonlocal integral boundary condition characteristics (poles, critical points, spectrum curves) and graphs characteristics (vertices, edges and faces) were found. The previous article
Jonas Vitkauskas, Artūras Štikonas
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Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2013 The boundary value problem for mixed type equation with nonlocal initial conditions in integral form is considered. The main result states that the nonlocal problem is equivalent to the classical boundary value problem for a loaded equation.
Svetlana V Kirichenko
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Global existence of solution to a nonlocal parabolic problem modeling linear friction welding [PDF]
, 2012 We study a nonlocal parabolic problem airing in the modeling of linear friction welding. Using some a priori estimates, we derive the global in time existence of solution of this nonlocal problem ...
Guo, Lin Yung-Jen +4 more
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