Blow-up Properties of a Coupled System of Reaction-Diffusion Equations

Rasheed, Maan A.

doi:10.24996/ijs.2021.62.9.20

Cited by 5 publications

(4 citation statements)

References 9 publications

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“…This article aims to discover the notion of 𝜕𝛩 * 𝐸𝐺𝑅𝑂 -detectability by means of the sensors selection [13][14][15]. The motive of studying conception, there are existent several problems in the real world need to be studied as in [16][17] and for another system types (see [18][19][20]). This means, one maybe devoted to the boundary gradient exponential problem of type detection in 𝜕𝛩 * (see Figure 1) [21].…”

Section: Introductionmentioning

confidence: 99%

Boundary Exponential Gradient Reduced Order Detectability in Neumann Conditions

Al-Bayati,

Al-Shaya,

Al-Saphory

2024

Iraqi Journal of Science

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This work, aims to study and examine the description f the gradient reduced order-strategic sensors of type boundary exponential (-strategic sensors) for completion gradient order-detectability of type boundary exponential (-detectability). Thus, this concept is linked to an estimator in distributed parameter systems (DPSS) in Neumann problem. So,we present numerous consequences regarding to diverse kinds of information, region and conditions of boundary region to allow existence of -detectable systems. In addition,we have estimated at the junction interface that the interior solution isharmonizedwith the exterior solution for -detectable and, we give the relationship between this concept and sensors structures. Finally,we demonstrate some applications with many circumstances f sensor positions.

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Section: Introductionmentioning

confidence: 99%

Boundary Exponential Gradient Reduced Order Detectability in Neumann Conditions

Al-Bayati,

Al-Shaya,

Al-Saphory

2024

Iraqi Journal of Science

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“…There is a large number of semilinear partial differential equations of the parabolic type whose solution for a given initial data cannot be extended globally in time and becomes unbounded in finite time. This phenomenon is called blow-up, and it can occur in semilinear equations, if the heat source is strong enough, see [1][2][3][4].…”

Section: Introductionmentioning

confidence: 99%

Numerical Blow-up Time of a One-Dimensional Semilinear Parabolic Equation with a Gradient Term

Rasheed

Hameed

Khalaf

2023

Iraqi Journal of Science

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This paper deals with numerical approximations of a one-dimensional semilinear parabolic equation with a gradient term. Firstly, we derive the semidiscrete problem of the considered problem and discuss its convergence and blow-up properties. Secondly, we propose both Euler explicit and implicit finite differences methods with a non-fixed time-stepping procedure to estimate the numerical blow-up time of the considered problem. Finally, two numerical experiments are given to illustrate the efficiency, accuracy, and numerical order of convergence of the proposed schemes.

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“…Therefore, since the last decades, the analytical and numerical solutions of partial differential equations have been studied by many authors, see for instance [17,20]. One of the remarkable phenomena in time-dependent problems is the blow-up; which has been considered by many authors (for a single equation and systems), see for instance [18,21,22].…”

Section: Introductionmentioning

confidence: 99%

https://www.isr-publications.com/jmcs/articles-12886-numerical-finite-difference-approximations-of-a-coupled-parabolic-system-with-blow-up

Khalil,

Hashim,

Rasheed

et al. 2023

J. Math. Computer Sci.

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This paper is concerned with the numerical blow-up time for a coupled system of two one-dimensional semilinear parabolic equations with zero Dirichlet boundary conditions. Firstly, we derive the semi-discrete problem and prove that the blow-up solution and numerical blow-up time of the semi-discrete problem are convergent to the theoretical ones, as we refine the spacetime grids. Secondly, we derive two fully discrete formulas of standard finite difference methods: the explicit Euler and implicit Euler schemes, with non-fixed time-stepping formula. In addition, we investigate the consistency, stability and convergence of the proposed schemes. Finally, we conduct two numerical experiments to show the accuracy and efficiency of the proposed schemes. Namely, for each experiment, we use the proposed schemes to calculate the numerical blow-up time, error bounds and the numerical order of convergence for blow-up times.

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Blow-up Properties of a Coupled System of Reaction-Diffusion Equations

Cited by 5 publications

References 9 publications

Boundary Exponential Gradient Reduced Order Detectability in Neumann Conditions

Boundary Exponential Gradient Reduced Order Detectability in Neumann Conditions

Numerical Blow-up Time of a One-Dimensional Semilinear Parabolic Equation with a Gradient Term

https://www.isr-publications.com/jmcs/articles-12886-numerical-finite-difference-approximations-of-a-coupled-parabolic-system-with-blow-up

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