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Quenching for discretization of a nonlinear diffusion equation with singular boundary flux
NGuessan Koffi,Anoh Assiedou Rodrigue,Coulibaly Adama,Toure Kidjegbo Augustin 원광대학교 기초자연과학연구소 2022 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.23 No.1
In this paper, we study the discrete approximation for the following nonlinear diffusion equation with nonlinear source and singular boundary flux $$\\ \left\{% \begin{array}{ll} \hbox{$\dfrac{\partial A(u)}{\partial t}=u_{xx} + (1-u)^{-\alpha}, \quad 0<x<1,\; t>0$,} \\ \hbox{$u_{x}(0,t)= 0, \quad u_{x}(1,t)=-B(u(1,t)),\quad t>0$,} \\ \hbox{$u(x,0)=u_{0}(x),\quad 0\leq x \leq 1$,} \\ \end{array}% \right. $$ with $ \alpha > 0. $ We find some conditions under which the solution of a discrete form of above problem quenches in a finite time and estimate its discrete quenching time. We also establish the convergence of the discrete quenching time to the theoretical one when the mesh size tends to zero. Finally, we give some numerical experiments for a best illustration of our analysis.
Camara Gninlfan Modeste,N’Guessan Koffi,Coulibaly Adama,Toure Kidjegbo Augustin 원광대학교 기초자연과학연구소 2021 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.22 No.3
This paper concerns the study of the numerical approximation for the following initial-boundary value problem .$$\left\{% \begin{array}{ll} \hbox{$u_t=\left( \vert u_{x}\vert^{p-2}u_{x}\right)_{x} + \left( 1-u\right)^{-h} ,\quad 0<x<1,\; t>0$,} \\ \hbox{$u_{x}(0,t)=0, \quad u_{x}(1,t)= - u^{-q}(1,t),\quad t>0$,} \\ \hbox{$u(x,0)=u_{0}(x) > 0,\quad 0\leq x \leq 1$,} \\ \end{array}% \right. $$ where $p\geq 2$, $h>0$, $q>0$. $u_{0}: [0,1] \rightarrow (0,1)$ and satisfies compatiblity conditions. We find some conditions under which the solution of a discrete form of above problem quenches in a finite time and estimate its discrete quenching time. We also establish the convergence of the discrete quenching time to the theoretical one when the mesh size tends to zero. Finally, we give some numerical experiments for a best illustration of our analysis.
Quenching for discretization of a semilinear heat equation with singular boundary outflux
Anoh Assiedou Rodrigue,N'Guessan Koffi,Coulibaly Adama,Toure Kidjegbo Augustin 원광대학교 기초자연과학연구소 2021 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.22 No.2
This paper concerns the study of the discret approximation for the following semilinear heat equation with a singular boundary outflux $$\\ \left\{% \begin{array}{ll} \hbox{$\dfrac{\partial u}{\partial t}=u_{xx} + (1-u)^{-p}, \quad 0<x<1,\; t>0$,} \\ \hbox{$u_{x}(0,t)= 0, \quad u_{x}(1,t)=-u(1,t)^{-q},\quad t>0$,} \\ \hbox{$u(x,0)=u_{0}(x),\quad 0\leq x \leq 1$,} \\ \end{array}% \right.$$ where $ p>0, $ $ q > 0. $ We find some conditions under which the solution of a discrete form of above problem quenches in a finite time and estimate its discrete quenching time. We also establish the convergence of the discrete quenching time to the theoretical one when the mesh size tends to zero. Finally, we give some numerical experiments for a best illustration of our analysis.
Proposed Message Transit Buffer Management Model for Nodes in Vehicular Delay-Tolerant Network
Gballou Yao, Theophile,Kimou Kouadio, Prosper,Tiecoura, Yves,Toure Kidjegbo, Augustin International Journal of Computer ScienceNetwork S 2023 International journal of computer science and netw Vol.23 No.1
This study is situated in the context of intelligent transport systems, where in-vehicle devices assist drivers to avoid accidents and therefore improve road safety. The vehicles present in a given area form an ad' hoc network of vehicles called vehicular ad' hoc network. In this type of network, the nodes are mobile vehicles and the messages exchanged are messages to warn about obstacles that may hinder the correct driving. Node mobilities make it impossible for inter-node communication to be end-to-end. Recognizing this characteristic has led to delay-tolerant vehicular networks. Embedded devices have small buffers (memory) to hold messages that a node needs to transmit when no other node is within its visibility range for transmission. The performance of a vehicular delay-tolerant network is closely tied to the successful management of the nodes' transit buffer. In this paper, we propose a message transit buffer management model for nodes in vehicular delay tolerant networks. This model consists in setting up, on the one hand, a policy of dropping messages from the buffer when the buffer is full and must receive a new message. This drop policy is based on the concept of intermediate node to destination, queues and priority class of service. It is also based on the properties of the message (size, weight, number of hops, number of replications, remaining time-to-live, etc.). On the other hand, the model defines the policy for selecting the message to be transmitted. The proposed model was evaluated with the ONE opportunistic network simulator based on a 4000m x 4000m area of downtown Bouaké in Côte d'Ivoire. The map data were imported using the Open Street Map tool. The results obtained show that our model improves the delivery ratio of security alert messages, reduces their delivery delay and network overload compared to the existing model. This improvement in communication within a network of vehicles can contribute to the improvement of road safety.
Ganon Ardjouma,N'Dri Kouakou Cyrille,Edja Kouame Beranger,Toure Kidjegbo Augustin 원광대학교 기초자연과학연구소 2023 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.26 No.3
This work is concerned with the study of the numerical approximation for the nonlinear diffusion equation $(u^{m})_t=u_{xx}$, $0<x<1, t>0$, with a singular boundary outfluxes $u_x(0,t)=u^{-p}(0,t)$, $u_x(1,t)=-u^{-q}(1,t)$, $t>0$. We use the finite differences method to obtain a semidiscrete scheme of the above problem. First, we give appropriate conditions under which the semidiscrete solution quenches in a finite time and estimate its semidiscrete quenching time. Then, we establish the convergence of the semidiscrete quenching time. Finally, we illustrate our analysis with some numerical experiments.