Zobrazeno 1 - 10
of 2 113
pro vyhledávání: '"allen-cahn equation"'
Publikováno v:
AIMS Mathematics, Vol 9, Iss 7, Pp 19332-19344 (2024)
The Allen-Cahn (AC) model is a mathematical equation that represents the phase separation process. The AC equation has numerous applications in various disciplines, such as image processing, physics, and biology. It models phase transitions, such as
Externí odkaz:
https://doaj.org/article/1df5067a7fa946669aede4c25cee3f1e
Autor:
Sakineh Hajiaghasi, Shahroud Azami
Publikováno v:
Sahand Communications in Mathematical Analysis, Vol 21, Iss 1, Pp 83-98 (2024)
In this paper, we consider positive solutions for the Allen-Cahn equation\begin{equation*}\Delta u+\left(1-u^{2}\right)u=0,\end{equation*}on an almost Ricci soliton without a boundary. Firstly, using volume comparison Theorem and Sobolev inequality,
Externí odkaz:
https://doaj.org/article/039e1fa69a7a45c8bd4e915f2649e000
Publikováno v:
AIMS Mathematics, Vol 9, Iss 1, Pp 735-762 (2024)
In this paper, we propose an explicit spatially fourth-order accurate compact scheme for the Allen-Cahn equation in one-, two-, and three-dimensional spaces. The proposed method is based on the explicit Euler time integration scheme and fourth-order
Externí odkaz:
https://doaj.org/article/8a6b9337685a4ab2b18079a7d796498f
Publikováno v:
Partial Differential Equations in Applied Mathematics, Vol 9, Iss , Pp 100653- (2024)
In this study, the Lie point symmetries and optimal system have been established. We discuss the biofilm model’s soliton solutions. To examine a nonlinear dynamical biofilm system, which is simply a bistable Allen–Cahn equation with quartic poten
Externí odkaz:
https://doaj.org/article/e4c290cee5284acd8e27a59d7108fabe
Publikováno v:
Communications in Analysis and Mechanics, Vol 15, Iss 4, Pp 611-637 (2023)
In this paper, we investigate the local discontinuous Galerkin (LDG) finite element method for the fractional Allen-Cahn equation with Caputo-Hadamard derivative in the time domain. First, the regularity of the solution is analyzed, and the results i
Externí odkaz:
https://doaj.org/article/a063a1abdcd14c79b006eee250859605
Publikováno v:
International Journal of Mathematical, Engineering and Management Sciences, Vol 8, Iss 5, Pp 912-926 (2023)
Stochastic fractional differential equations are among the most significant and recent equations in physical mathematics. Consequently, several scholars have recently been interested in these equations to develop analytical approximations. In this st
Externí odkaz:
https://doaj.org/article/3ffab999867b45f1a7f192cc2ecbb036
Publikováno v:
Electronic Research Archive, Vol 31, Iss 8, Pp 5104-5123 (2023)
In this study, we present an efficient and novel unconditionally stable Monte Carlo simulation (MCS) for solving the multi-dimensional Allen–Cahn (AC) equation, which can model the motion by mean curvature flow of a hypersurface. We use an operator
Externí odkaz:
https://doaj.org/article/7002c289ecf84a81a3fa902a3661eaf3
Autor:
Dongsun Lee
Publikováno v:
AIMS Mathematics, Vol 8, Iss 10, Pp 23352-23371 (2023)
The Allen-Cahn equation is a famous nonlinear reaction-diffusion equation used to study geometric motion and minimal hypersurfaces. This link has been scrutinized to construct minimal surfaces for many years. The shape of soap film is very interestin
Externí odkaz:
https://doaj.org/article/17f52395488d4d3eac35417d805e5398