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Discrete and Continuous Dynamical Systems- Series A, ISSN 1078-0947, 11/2018, Volume 38, Issue 11, pp. 5615 - 5648
In this paper, we prove a well posedness result for an initial boundary value problem for a stochastic nonlocal reaction-diffusion equation with nonlinear diffusion together with a nul-flux boundary... 
Monotonicity method | Stochastic nonlocal reaction-diffusion equation | Conservation of mass | MATHEMATICS | MATHEMATICS, APPLIED | monotonicity method | conservation of mass
Journal Article
Journal Article
Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, 06/2017, Volume 320, Issue C, pp. 46 - 67
In this paper, we first propose a nonlocal convection–diffusion model, in which the convection term is constructed in a special upwind manner so that mass conservation and maximum principle are maintained in any space dimension... 
Maximum principle | Asymptotically compatible | Quadrature-based finite difference | Mass conservation | Nonlocal convection–diffusion | VECTOR CALCULUS | ELEMENT-METHOD | APPROXIMATIONS | DISPERSION | DISCONTINUITIES | LONG-RANGE FORCES | Nonlocal convection-diffusion | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | PERIDYNAMIC MODELS | SOLID MECHANICS | BOUNDED DOMAINS | VOLUME-CONSTRAINED PROBLEMS | Mechanics | Engineering | Mathematics
Journal Article
Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, 06/2015, Volume 289, pp. 60 - 78
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 12/2015, Volume 432, Issue 1, pp. 398 - 428
In this paper we present a variational approach to establish the existence and uniqueness of variational solutions to nonlocal evolutionary problems. The model... 
Parabolic minimizer | Parabolic equations | Variational minimizer | Nonlocal partial differential equations | Existence of solutions | Analysis | Differential equations
Journal Article
Advances in Mathematics, ISSN 0001-8708, 06/2016, Volume 295, pp. 334 - 367
We study the global existence of solutions to a one-dimensional drift–diffusion equation with logistic term, generalizing the classical parabolic–elliptic Keller... 
Drift–diffusion equation | Global existence | Nonlocal diffusion | Drift-diffusion equation | MAXIMUM PRINCIPLE | FINITE-TIME SINGULARITIES | WELL-POSEDNESS | MODEL | MATHEMATICS | KELLER-SEGEL SYSTEM | NONLOCAL VELOCITY | MUSKAT PROBLEM | TRANSPORT-EQUATION | BLOW-UP | FRACTIONAL DIFFUSION | Mathematics - Analysis of PDEs
Journal Article
Computers and Mathematics with Applications, ISSN 0898-1221, 05/2019, Volume 77, Issue 9, pp. 2534 - 2552
Journal Article
Zeitschrift für angewandte Mathematik und Physik, ISSN 0044-2275, 2/2018, Volume 69, Issue 1, pp. 1 - 31
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 2009, Volume 247, Issue 2, pp. 511 - 529
...–diffusion equations with time delays. In this paper we will consider a nonlocal time-delayed reaction–diffusion equation... 
Stability | 92D25 | Time-delay | Traveling waves | 35K57 | Nonlocal reaction–diffusion equation | 34K20 | Nonlocal reaction-diffusion equation | MATHEMATICS | NICHOLSONS BLOWFLIES EQUATION | ASYMPTOTIC STABILITY | POPULATION-MODEL
Journal Article
Journal of the London Mathematical Society, ISSN 0024-6107, 04/2018, Volume 97, Issue 2, pp. 258 - 281
We consider a convection–diffusion model with linear fractional diffusion in the sub... 
35B40 (primary) | 26A33 (secondary) | NONLOCAL REGULARIZATION | MATHEMATICS | DIMENSIONS | CONSERVATION-LAWS | FRACTAL BURGERS-EQUATION | LARGE TIME BEHAVIOR | Mathematics - Analysis of PDEs
Journal Article