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Journal articles on the topic 'Nonlocal Neumann boundary conditions'

Author: Grafiati

Published: 10 March 2023

Last updated: 19 July 2025

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1

You, Huaiqian, Xin Yang Lu, Nathaniel Trask, and Yue Yu. "An asymptotically compatible approach for Neumann-type boundary condition on nonlocal problems." ESAIM: Mathematical Modelling and Numerical Analysis 55 (2021): S811—S851. http://dx.doi.org/10.1051/m2an/2020058.

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In this paper we consider 2D nonlocal diffusion models with a finite nonlocal horizon parameter δ characterizing the range of nonlocal interactions, and consider the treatment of Neumann-like boundary conditions that have proven challenging for discretizations of nonlocal models. We propose a new generalization of classical local Neumann conditions by converting the local flux to a correction term in the nonlocal model, which provides an estimate for the nonlocal interactions of each point with points outside the domain. While existing 2D nonlocal flux boundary conditions have been shown to ex

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2

You, Huaiqian, XinYang Lu, Nathaniel Task, and Yue Yu. "An asymptotically compatible approach for Neumann-type boundary condition on nonlocal problems." ESAIM: Mathematical Modelling and Numerical Analysis 54, no. 4 (2020): 1373–413. http://dx.doi.org/10.1051/m2an/2019089.

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In this paper we consider 2D nonlocal diffusion models with a finite nonlocal horizon parameter δ characterizing the range of nonlocal interactions, and consider the treatment of Neumann-like boundary conditions that have proven challenging for discretizations of nonlocal models. We propose a new generalization of classical local Neumann conditions by converting the local flux to a correction term in the nonlocal model, which provides an estimate for the nonlocal interactions of each point with points outside the domain. While existing 2D nonlocal flux boundary conditions have been shown to ex

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3

Dipierro, Serena, Xavier Ros-Oton, and Enrico Valdinoci. "Nonlocal problems with Neumann boundary conditions." Revista Matemática Iberoamericana 33, no. 2 (2017): 377–416. http://dx.doi.org/10.4171/rmi/942.

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4

Turmetov, B. Kh, and V. V. Karachik. "NEUMANN BOUNDARY CONDITION FOR A NONLOCAL BIHARMONIC EQUATION." Bulletin of the South Ural State University series "Mathematics. Mechanics. Physics" 14, no. 2 (2022): 51–58. http://dx.doi.org/10.14529/mmph220205.

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The solvability conditions for a class of boundary value problems for a nonlocal biharmonic equation in the unit ball with the Neumann conditions on the boundary are studied. The nonlocality of the equation is generated by some orthogonal matrix. The presence and uniqueness of a solution to the proposed Neumann boundary condition is examined, and an integral representation of the solution to the Dirichlet problem in terms of the Green's function for the biharmonic equation in the unit ball is obtained. First, some auxiliary statements are established: the Green's function of the Dirichlet prob

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5

Bogoya, Mauricio, and Cesar A. Gómez S. "On a nonlocal diffusion model with Neumann boundary conditions." Nonlinear Analysis: Theory, Methods & Applications 75, no. 6 (2012): 3198–209. http://dx.doi.org/10.1016/j.na.2011.12.019.

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6

Aksoylu, Burak, and Fatih Celiker. "Nonlocal problems with local Dirichlet and Neumann boundary conditions." Journal of Mechanics of Materials and Structures 12, no. 4 (2017): 425–37. http://dx.doi.org/10.2140/jomms.2017.12.425.

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7

Sharafidinov, D. D., and B. Kh Turmetov. "ON THE SOLVABILITY OF CERTAIN INITIAL-BOUNDARY VALUE PROBLEMS FOR A NONLOCAL HYPERBOLIC EQUATION." Q A Iasaýı atyndaǵy Halyqaralyq qazaq-túrіk ýnıversıtetіnіń habarlary (fızıka matematıka ınformatıka serııasy) 31, no. 4 (2024): 7–18. https://doi.org/10.47526/2024-4/2524-0080.12.

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This paper investigates the well-posedness of initial-boundary value problems for a nonlocal analogue of the hyperbolic equation. The elliptic part of the considered equations involves a nonlocal analogue of the Laplace operator. We find the eigenfunctions and eigenvalues of boundary value problems for a nonlocal analogue of the Laplace operator. The eigenfunctions of the problems are represented as even and odd parts with respect to the considered mapping. The symmetry properties of the eigenfunctions of boundary value problems with Dirichlet and Neumann conditions are investigated. These pro

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8

Karachik, Valery, Batirkhan Turmetov, and Hongfen Yuan. "Four Boundary Value Problems for a Nonlocal Biharmonic Equation in the Unit Ball." Mathematics 10, no. 7 (2022): 1158. http://dx.doi.org/10.3390/math10071158.

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Solvability issues of four boundary value problems for a nonlocal biharmonic equation in the unit ball are investigated. Dirichlet, Neumann, Navier and Riquier–Neumann boundary value problems are studied. For the problems under consideration, existence and uniqueness theorems are proved. Necessary and sufficient conditions for the solvability of all problems are obtained and an integral representations of solutions are given in terms of the corresponding Green’s functions.

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9

Gomez, C. A., and J. A. Caicedo. "ON A RESCALED NONLOCAL DIFFUSION PROBLEM WITH NEUMANN BOUNDARY CONDITIONS." Advances in Mathematics: Scientific Journal 10, no. 8 (2021): 3013–22. http://dx.doi.org/10.37418/amsj.10.8.2.

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In this work, we consider the rescaled nonlocal diffusion problem with Neumann Boundary Conditions \[ \begin{cases} u_t^{\epsilon}(x,t)=\displaystyle\frac{1}{\epsilon^2} \int_{\Omega}J_{\epsilon}(x-y)(u^\epsilon(y,t)-u^\epsilon(x,t))dy\\ \qquad \qquad+\displaystyle\frac{1}{\epsilon}\int_{\partial \Omega}G_\epsilon(x-y)g(y,t)dS_y,\\ u^\epsilon(x,0)=u_0(x), \end{cases} \] where $\Omega\subset\mathbb{R}^{N}$ is a bounded, connected and smooth domain, $g$ a positive continuous function, $J_\epsilon(z)=C_1\frac{1}{\epsilon^N}J(\frac{z}{\epsilon}), G_\epsilon(x)=C_1\frac{1}{\epsilon^N}G(\frac{x}{\ep

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10

Agarwal, Praveen, Jochen Merker, and Gregor Schuldt. "Singular Integral Neumann Boundary Conditions for Semilinear Elliptic PDEs." Axioms 10, no. 2 (2021): 74. http://dx.doi.org/10.3390/axioms10020074.

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In this article, we discuss semilinear elliptic partial differential equations with singular integral Neumann boundary conditions. Such boundary value problems occur in applications as mathematical models of nonlocal interaction between interior points and boundary points. Particularly, we are interested in the uniqueness of solutions to such problems. For the sublinear and subcritical case, we calculate, on the one hand, illustrative, rather explicit solutions in the one-dimensional case. On the other hand, we prove in the general case the existence and—via the strong solution of an integro-P

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11

Karachik, V. V. "THE BIHARMONIC NEUMANN PROBLEM WITH DOUBLE INVOLUTION." Bulletin of the South Ural State University series "Mathematics. Mechanics. Physics" 16, no. 3 (2024): 18–26. https://doi.org/10.14529/mmph240303.

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This paper studies the solvability of a new class of boundary value problems with nonlocal Neumann conditions for a biharmonic equation in a sphere. Non-local conditions are specified in the form of a connection between the values of the desired function at different points of the boundary. In this case, the boundary operator is determined using matrices of involution-type mappings. The theorem of existence the and uniqueness of the solution is proved and the integral representation of the solution to the problem under consideration is found.

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12

Da Lio, Francesca, Christina Inwon Kim, and Dejan Slepčev. "Nonlocal front propagation problems in bounded domains with Neumann‐type boundary conditions and applications." Asymptotic Analysis 37, no. 3-4 (2004): 257–92. https://doi.org/10.3233/asy-2004-609.

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This paper is concerned with the asymptotic behavior as ε→0 of the solutions of nonlocal reaction–diffusion equations of the form ut−Δu+ε−2f(u,ε∫0u)=0 in O×(0,T) associated with nonlinear oblique derivative boundary conditions. We show that such behavior is described in terms of an interface evolving with normal velocity depending not only on its curvature but also on the measure of the set it encloses. To this purpose we introduce a weak notion of motion of hypersurfaces with nonlocal normal velocities depending on the volume they enclose, which extends the geometric definition of generalized

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13

Andreu, F., J. M. Mazón, J. D. Rossi, and J. Toledo. "A nonlocal p-Laplacian evolution equation with Neumann boundary conditions." Journal de Mathématiques Pures et Appliquées 90, no. 2 (2008): 201–27. http://dx.doi.org/10.1016/j.matpur.2008.04.003.

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14

Yildirim, Ozgur. "On stable high order difference schemes for hyperbolic problems with the Neumann boundary conditions." An International Journal of Optimization and Control: Theories & Applications (IJOCTA) 9, no. 1 (2019): 60–72. http://dx.doi.org/10.11121/ijocta.01.2019.00592.

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In this paper, third and fourth order of accuracy stable difference schemes for approximately solving multipoint nonlocal boundary value problems for hyperbolic equations with the Neumann boundary conditions are considered. Stability estimates for the solutions of these difference schemes are presented. Finite difference method is used to obtain numerical solutions. Numerical results of errors and CPU times are presented and are analyzed.

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15

Zhang, Wei, Jiang Yang, Jiwei Zhang, and Qiang Du. "Artificial Boundary Conditions for Nonlocal Heat Equations on Unbounded Domain." Communications in Computational Physics 21, no. 1 (2016): 16–39. http://dx.doi.org/10.4208/cicp.oa-2016-0033.

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AbstractThis paper is concerned with numerical approximations of a nonlocal heat equation define on an infinite domain. Two classes of artificial boundary conditions (ABCs) are designed, namely, nonlocal analog Dirichlet-to-Neumann-type ABCs (global in time) and high-order Padé approximate ABCs (local in time). These ABCs reformulate the original problem into an initial-boundary-value (IBV) problem on a bounded domain. For the global ABCs, we adopt a fast evolution to enhance computational efficiency and reduce memory storage. High order fully discrete schemes, both second-order in time and sp

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16

Boussaïd, Samira. "UNIVERSAL ATTRACTOR FOR A NONLOCAL REACTION-DIFFUSION PROBLEM WITH DYNAMICAL BOUNDARY CONDITIONS." Advances in Mathematics: Scientific Journal 11, no. 9 (2022): 789–801. http://dx.doi.org/10.37418/amsj.11.9.4.

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A nonlocal reaction-diffusion equation is presented in this article, based on a model proposed by J. Rubinstein and P. Sternberg [6] with a nonlinear strictly monotone operator. A dynamical boundary condition is considered, rather then the usual ones such as Neumann or Dirichlet boundary conditions. The well-posedness and the existence of a universal attractor of this problem, which describes the long time behavior of the solution, are established.

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17

Dadabayeva, F. A., and B. Kh Turmetov. "On eigenfunctions and eigenvalues of some boundary value problems for a nonlocal biharmonic operator." Q A Iasaýı atyndaǵy Halyqaralyq qazaq-túrіk ýnıversıtetіnіń habarlary (fızıka matematıka ınformatıka serııasy) 26, no. 3 (2023): 39–62. http://dx.doi.org/10.47526/2023-3/2524-0080.03.

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In this note, the concept of a nonlocal biharmonic operator is introduced. When introducing this operator, mappings of the type of involution are used. Namely, in the differential expression of this operator, in addition to the variables 12( , ,..., )nxx xx, transformed arguments with mappings of the form 111,...,,,,...,,1jjjjjnS xxxpx xxj n and their multiplication also involved. Spectral problems with Dirichlet and Neumann-type boundary conditions are considered in an n-dimensional parallelepiped for a given nonlocal biharmonic operator. The eigenfunctions and eigenvalues of the pro

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18

Barbu, Tudor, Alain Miranville, and Costică Moroşanu. "On a Local and Nonlocal Second-Order Boundary Value Problem with In-Homogeneous Cauchy–Neumann Boundary Conditions—Applications in Engineering and Industry." Mathematics 12, no. 13 (2024): 2050. http://dx.doi.org/10.3390/math12132050.

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A qualitative study for a second-order boundary value problem with local or nonlocal diffusion and a cubic nonlinear reaction term, endowed with in-homogeneous Cauchy–Neumann (Robin) boundary conditions, is addressed in the present paper. Provided that the initial data meet appropriate regularity conditions, the existence of solutions to the nonlocal problem is given at the beginning in a function space suitably chosen. Next, under certain assumptions on the known data, we prove the well posedness (the existence, a priori estimates, regularity, uniqueness) of the classical solution to the loca

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19

Patlashenko, Igor, and Dan Givoli. "Non-Reflecting Finite Element Schemes for Three-Dimensional Acoustic Waves." Journal of Computational Acoustics 05, no. 01 (1997): 95–115. http://dx.doi.org/10.1142/s0218396x97000071.

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The finite element solution of problems involving three-dimensional acoustic waves in an infinite wave guide, and in the infinite medium around a structure is considered. Such problems are typical in structural acoustics, and this paper concentrates on the efficient numerical treatment of the infinite acoustic medium away from the structure. The unbounded domain is truncated by means of an artificial boundary ℬ. On ℬ, non-reflecting boundary conditions are used; these are either nonlocal Dirichlet-to-Neumann conditions, or their localized counterparts. For the high-order localized conditions,

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20

Niculescu, Constantin P., and Ionel Rovenţa. "Large Solutions for Semilinear Parabolic Equations Involving Some Special Classes of Nonlinearities." Discrete Dynamics in Nature and Society 2010 (2010): 1–11. http://dx.doi.org/10.1155/2010/491023.

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We consider a new class of nonlinearities for which a nonlocal parabolic equation with Neumann boundary conditions has finite time blow-up solutions. Our approach is inspired by previous work done by Jazar and Kiwan (2008) and El Soufi et al. (2007).

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21

Montagu, E. L., and John Norbury. "Solution Structure for Nonautonomous Nonlocal Elliptic Equations with Neumann Boundary Conditions." Integral Transforms and Special Functions 13, no. 5 (2002): 461–70. http://dx.doi.org/10.1080/10652460213527.

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22

Barles, Guy, Christine Georgelin, and Espen R. Jakobsen. "On Neumann and oblique derivatives boundary conditions for nonlocal elliptic equations." Journal of Differential Equations 256, no. 4 (2014): 1368–94. http://dx.doi.org/10.1016/j.jde.2013.11.001.

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23

Chabrowski, J. "On bi-nonlocal problem for elliptic equations with Neumann boundary conditions." Journal d'Analyse Mathématique 134, no. 1 (2018): 303–34. http://dx.doi.org/10.1007/s11854-018-0011-5.

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24

Turmetov, Batirkhan, Valery Karachik, and Moldir Muratbekova. "On a Boundary Value Problem for the Biharmonic Equation with Multiple Involutions." Mathematics 9, no. 17 (2021): 2020. http://dx.doi.org/10.3390/math9172020.

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A nonlocal analogue of the biharmonic operator with involution-type transformations was considered. For the corresponding biharmonic equation with involution, we investigated the solvability of boundary value problems with a fractional-order boundary operator having a derivative of the Hadamard-type. First, transformations of the involution type were considered. The properties of the matrices of these transformations were investigated. As applications of the considered transformations, the questions about the solvability of a boundary value problem for a nonlocal biharmonic equation were studi

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25

Koshanova, M., М. Muratbekova, and B. Turmetov. "SOME BOUNDARY VALUE PROBLEMS WITH INVOLUTION FOR THE NONLOCAL POISSON EQUATION." BULLETIN Series of Physics & Mathematical Sciences 71, no. 3 (2020): 74–83. http://dx.doi.org/10.51889/2020-3.1728-7901.10.

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In this paper, we study new classes of boundary value problems for a nonlocal analogue of the Poisson equation. The boundary conditions, as well as the nonlocal Poisson operator, are specified using transformation operators with orthogonal matrices. The paper investigates the questions of solvability of analogues of boundary value problems of the Dirichlet and Neumann type. It is proved that, as in the classical case, the analogue of the Dirichlet problem is unconditionally solvable. For it, theorems on the existence and uniqueness of the solution to the problem are proved. An explicit form of

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26

XUE, Yingzhen. "Lower Bounds of Blow Up Time for a Class of Slow Reaction Diffusion Equations with Inner Absorption Terms." Wuhan University Journal of Natural Sciences 28, no. 5 (2023): 373–78. http://dx.doi.org/10.1051/wujns/2023285373.

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In this paper, a class of slow reaction-diffusion equations with nonlocal source and inner absorption terms are studied. By using the technique of improved differential inequality, the lower bounds of blow up time for the system under either homogeneous Dirichlet or nonhomogeneous Neumann boundary conditions are obtained.

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27

Turmetov, B. Kh. "On solvability of some boundary value problems for a nonlocal Poisson equation with periodic conditions." Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki 35, no. 1 (2025): 137–54. https://doi.org/10.35634/vm250109.

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In the present paper, a nonlocal analog of the Laplace operator is introduced by means of involution-type mappings. New classes of boundary value problems are studied for the corresponding nonlocal analog of the Poisson equation in a unit sphere. In the problems under consideration, the boundary conditions are given in the form of a relation between the value of the unknown function in the upper hemisphere and the value in the lower hemisphere. The problems under study generalize the known periodic and antiperiodic boundary value problems for circular regions. The problems are solved by reduci

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28

Heidari, Samira, and Abdolrahman Razani. "Infinitely many solutions for nonlocal elliptic systems in Orlicz–Sobolev spaces." Georgian Mathematical Journal 29, no. 1 (2021): 45–54. http://dx.doi.org/10.1515/gmj-2021-2110.

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Abstract Recently, the existence of at least two weak solutions for a Kirchhoff–type problem has been studied in [M. Makvand Chaharlang and A. Razani, Two weak solutions for some Kirchhoff-type problem with Neumann boundary condition, Georgian Math. J. 28 2021, 3, 429–438]. Here, the existence of infinitely many solutions for nonlocal Kirchhoff-type systems including Dirichlet boundary conditions in Orlicz–Sobolev spaces is studied by using variational methods and critical point theory.

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29

Karachik, Valery, and Batirkhan Turmetov. "On solvability of some nonlocal boundary value problems for biharmonic equation." Mathematica Slovaca 70, no. 2 (2020): 329–42. http://dx.doi.org/10.1515/ms-2017-0355.

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Abstract In this paper a new class of well-posed boundary value problems for the biharmonic equation is studied. The considered problems are nonlocal boundary value problems of Bitsadze- -Samarskii type. These problems are solved by reducing them to Dirichlet and Neumann type problems. Theorems on existence and uniqueness of the solution are proved and exact solvability conditions of the considered problems are found. In addition, the integral representations of solutions are obtained.

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30

Andreu, F., J. M. Mazón, J. D. Rossi, and J. Toledo. "Local and nonlocal weighted $p$-Laplacian evolution equations with Neumann boundary conditions." Publicacions Matemàtiques 55 (January 1, 2011): 27–66. http://dx.doi.org/10.5565/publmat_55111_03.

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31

Yang, Fei-Ying, Wan-Tong Li, and Shigui Ruan. "Dynamics of a nonlocal dispersal SIS epidemic model with Neumann boundary conditions." Journal of Differential Equations 267, no. 3 (2019): 2011–51. http://dx.doi.org/10.1016/j.jde.2019.03.001.

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32

Afrouzi, Ghasem A., Z. Naghizadeh, and Nguyen Thanh Chung. "Multiple solutions for a class of bi-nonlocal problems with nonlinear Neumann boundary conditions." Boletim da Sociedade Paranaense de Matemática 40 (January 18, 2022): 1–11. http://dx.doi.org/10.5269/bspm.44144.

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In this paper, we are interested in a class of bi-nonlocal problems with nonlinear Neumann boundary conditions and sublinear terms at infinity. Using $(S_+)$ mapping theory and variational methods, we establish the existence of at least two non-trivial weak solutions for the problem provied that the parameters are large enough. Our result complements and improves some previous ones for the superlinear case when the Ambrosetti-Rabinowitz type conditions are imposed on the nonlinearities.

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33

Esposito, Giampiero, and Giuseppe Pollifrone. "Noncovariant Gauges in Simple Supergravity." International Journal of Modern Physics D 06, no. 04 (1997): 479–90. http://dx.doi.org/10.1142/s0218271897000285.

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A gauge-averaging functional of the axial type is studied for simple supergravity at one loop about flat Euclidean four-space bounded by a three-sphere, or two concentric three-spheres. This is a generalization of recent work on the axial gauge in quantum supergravity on manifolds with boundary. Ghost modes obey nonlocal boundary conditions of the spectral type, in that half of them obey Dirichlet or Neumann conditions at the boundary. In both cases, they give a vanishing contribution to the one-loop divergence. The admissibility of noncovariant gauges at the classical level is also proved.

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Ashyralyyev, C., and A. Cay. "Numerical solution to elliptic inverse problem with Neumann-type integral condition and overdetermination." BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS 99, no. 3 (2020): 5–17. http://dx.doi.org/10.31489/2020m3/5-17.

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In modeling various real processes, an important role is played by methods of solution source identification problem for partial differential equation. The current paper is devoted to approximate of elliptic over determined problem with integral condition for derivatives. In the beginning, inverse problem is reduced to some auxiliary nonlocal boundary value problem with integral boundary condition for derivatives. The parameter of equation is defined after solving that auxiliary nonlocal problem. The second order of accuracy difference scheme for approximately solving abstract elliptic overdet

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35

Bouziani, Abdelfatah. "Initial-boundary value problem with a nonlocal condition for a viscosity equation." International Journal of Mathematics and Mathematical Sciences 30, no. 6 (2002): 327–38. http://dx.doi.org/10.1155/s0161171202004167.

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This paper deals with the proof of the existence, uniqueness, and continuous dependence of a strong solution upon the data, for an initial-boundary value problem which combine Neumann and integral conditions for a viscosity equation. The proof is based on an energy inequality and on the density of the range of the linear operator corresponding to the abstract formulation of the studied problem.

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PATLASHENKO, IGOR, and DAN GIVOLI. "OPTIMAL LOCAL NONREFLECTING BOUNDARY CONDITIONS FOR TIME-DEPENDENT WAVES." Journal of Computational Acoustics 08, no. 01 (2000): 157–70. http://dx.doi.org/10.1142/s0218396x00000108.

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Nonreflecting Boundary Conditions (NRBCs) are often used on artificial boundaries as a method for the numerical solution of wave problems in unbounded domains. Recently, a two-parameter hierarchy of optimal local NRBCs of increasing order has been developed for elliptic problems, including the problem of time-harmonic acoustic waves. The optimality is in the sense that the local NRBC best approximates the exact nonlocal Dirichlet-to-Neumann (DtN) boundary condition in the L2 norm for functions which can be Fourier-decomposed. The optimal NRBCs are combined with finite element discretization in

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37

Yuan, Yueding, and Zhiming Guo. "Global Asymptotic Stability in a Class of Reaction-Diffusion Equations with Time Delay." Abstract and Applied Analysis 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/378172.

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We study a very general class of delayed reaction-diffusion equations in which the reaction term can be nonmonotone and spatially nonlocal. By using a fluctuation method, combined with the careful analysis of the corresponding characteristic equations, we obtain some sufficient conditions for the global asymptotic stability of the trivial solution and the positive steady state to the equations subject to the Neumann boundary condition.

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Xiang, Zhaoyin, Qiong Chen, and Chunlai Mu. "Blowup properties for several diffusion systems with localised sources." ANZIAM Journal 48, no. 1 (2006): 37–56. http://dx.doi.org/10.1017/s1446181100003400.

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AbstractThis paper investigates the Cauchy problem for two classes of parabolic systems with localised sources. We first give the blowup criterion, and then deal with the possibilities of simultaneous blowup or non-simultaneous blowup under some suitable assumptions. Moreover, when simultaneous blowup occurs, we also establish precise blowup rate estimates. Finally, using similar ideas and methods, we shall consider several nonlocal problems with homogeneous Neumann boundary conditions.

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39

Bogoya, Mauricio, Raul Ferreira, and Julio D. Rossi. "Neumann boundary conditions for a nonlocal nonlinear diffusion operator. Continuous and discrete models." Proceedings of the American Mathematical Society 135, no. 12 (2007): 3837–47. http://dx.doi.org/10.1090/s0002-9939-07-09205-2.

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40

Slepčev, Dejan. "Approximation schemes for propagation of fronts with nonlocal velocities and Neumann boundary conditions." Nonlinear Analysis: Theory, Methods & Applications 52, no. 1 (2003): 79–115. http://dx.doi.org/10.1016/s0362-546x(02)00098-6.

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41

Gómez, Cesar A., and Julio D. Rossi. "A nonlocal diffusion problem that approximates the heat equation with Neumann boundary conditions." Journal of King Saud University - Science 32, no. 1 (2020): 17–20. http://dx.doi.org/10.1016/j.jksus.2017.08.008.

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42

Liao, Menglan, and Wenjie Gao. "Blow-up phenomena for a nonlocal p-Laplace equation with Neumann boundary conditions." Archiv der Mathematik 108, no. 3 (2016): 313–24. http://dx.doi.org/10.1007/s00013-016-0986-z.

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43

Wang, Yulan, Zhaoyin Xiang, and Jinsong Hu. "Blowup Analysis for a Nonlocal Diffusion Equation with Reaction and Absorption." Journal of Applied Mathematics 2012 (2012): 1–17. http://dx.doi.org/10.1155/2012/648067.

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We investigate a nonlocal reaction diffusion equation with absorption under Neumann boundary. We obtain optimal conditions on the exponents of the reaction and absorption terms for the existence of solutions blowing up in finite time, or for the global existence and boundedness of all solutions. For the blowup solutions, we also study the blowup rate estimates and the localization of blowup set. Moreover, we show some numerical experiments which illustrate our results.

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44

Tian, Huimin, and Lingling Zhang. "Blow-up analyses in nonlocal reaction diffusion equations with time-dependent coefficients under Neumann boundary conditions." Open Mathematics 18, no. 1 (2020): 1552–64. http://dx.doi.org/10.1515/math-2020-0088.

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Abstract In this paper, the blow-up analyses in nonlocal reaction diffusion equations with time-dependent coefficients are investigated under Neumann boundary conditions. By constructing some suitable auxiliary functions and using differential inequality techniques, we show some sufficient conditions to ensure that the solution u ( x , t ) u(x,t) blows up at a finite time under appropriate measure sense. Furthermore, an upper and a lower bound on blow-up time are derived under some appropriate assumptions. At last, two examples are presented to illustrate the application of our main results.

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Turkyilmazoglu, Mustafa. "Hyperbolic Partial Differential Equations with Nonlocal Mixed Boundary Values and their Analytic Approximate Solutions." International Journal of Computational Methods 15, no. 02 (2017): 1850003. http://dx.doi.org/10.1142/s0219876218500032.

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Partial differential equations of hyperbolic type when considered with mixed Dirichlet/Neumann constraints as well as nonlocal conservation conditions model many physical phenomena. The prime motivation of the current work is to apply the recently developed meshfree method to such differential equations. The scheme is built on series expansion of the solution via proper base functions akin to the Galerkin approach. In many cases, the simple polynomials are adequate to convert the hyperbolic partial differential equation and boundary conditions of nonlocal kind into easily treatable algebraic e

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Bouziani, Abdelfatah. "On the Solvability of a Nonlocal Problem Arising in Dynamics of Moisture Transfer." gmj 10, no. 4 (2003): 607–22. http://dx.doi.org/10.1515/gmj.2003.607.

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Abstract In the recent years, evolution problems with an integral term in the boundary conditions have received a great deal of attention. Such problems, in general, are nonself-adjoint, and this poses the basic source of difficulty, which can considerably complicate the application of standard functional and numerical techniques. To avoid these complications, we have introduced a nonclassical function space to establish a priori estimates without any additional complication as compared to the classical evolution problems. As an example of the applicability of this way of solving problems of t

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De Luca, Alessandra, Veronica Felli, and Giovanni Siclari. "Strong Unique Continuation from the Boundary for the Spectral Fractional Laplacian." ESAIM: Control, Optimisation and Calculus of Variations 29 (2023): 50. http://dx.doi.org/10.1051/cocv/2023045.

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We investigate unique continuation properties and asymptotic behaviour at boundary points for solutions to a class of elliptic equations involving the spectral fractional Laplacian. An extension procedure leads us to study a degenerate or singular equation on a cylinder, with a homogeneous Dirichlet boundary condition on the lateral surface and a non-homogeneous Neumann condition on the basis. For the extended problem, by an Almgren-type monotonicity formula and a blow-up analysis, we classify the local asymptotic profiles at the edge where the transition between boundary conditions occurs. Pa

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Hameed, Raad, Boying Wu, and Jiebao Sun. "Periodic solution of a quasilinear parabolic equation with nonlocal terms and Neumann boundary conditions." Boundary Value Problems 2013, no. 1 (2013): 34. http://dx.doi.org/10.1186/1687-2770-2013-34.

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Cortazar, Carmen, Manuel Elgueta, Julio D. Rossi, and Noemi Wolanski. "How to Approximate the Heat Equation with Neumann Boundary Conditions by Nonlocal Diffusion Problems." Archive for Rational Mechanics and Analysis 187, no. 1 (2007): 137–56. http://dx.doi.org/10.1007/s00205-007-0062-8.

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Qu, Chengyuan, Xueli Bai, and Sining Zheng. "Blow-up versus extinction in a nonlocal p -Laplace equation with Neumann boundary conditions." Journal of Mathematical Analysis and Applications 412, no. 1 (2014): 326–33. http://dx.doi.org/10.1016/j.jmaa.2013.10.040.

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