Worst-case Analysis of Distributed Parameter Systems with Application to the 2D Reaction-Diffusion Equation. Optim. Contr. Appl. Met., 31, 433-449.Kishida, M., Braatz, R.D.: `Worst-case analysis of distributed param- eter systems with application to the 2D reaction-diffusion equation', ...
A reaction–diffusion equation with spatially anisotropic time delay, more general than (3), is considered below (see Equation (12)). For clarity, the procedure for constructing exact solutions to PDEs with anisotropic delay based on exact solutions of simpler PDEs with constant delay, which was...
In Section 2, for the sake of clarity, we consider a one-dimensional, time-dependent, nonlinear reaction–diffusion equation, and present several new approaches based on the Kirchhoff transformation and the heat potential, the energy per unit volume and the temperature. We then employ time ...
The space-time method has been used to solve some time-dependent issues, for example, the traditional continuous space-time finite element method for the heat equation [25], the reduced-order method combined with the space-time finite element method for the 2D Sobolev equation [26], a high-...
Equation (1) is used to convert theforce into strength in the unit of Pascal. yield strength=(yield force1000×g)/πr2yield strength=(yield force1000×g)/πr2 (1) where yield strength is the maximum strength when the sample rupture, yield force is the maximum force when the sample...
Through using boundary condition (4), Green’s formula and Lemma 2, the following equation can be obtained: 2 ∫ Ω ∑ i = 1 m e T ( t , x ) ( I N ⊗ P 1 ) ( I N ⊗ D ) ∂ 2 e ( t , x ) ∂ x l 2 d x = 2 ∫ Ω ∑ i = 1 m e T ( t , x ...
Lyu and Vong [26] proposed a high-order method to resolve a time-fractional Benjamin–Bona–Mahony equation over a nonuniform temporal mesh. Stynes et al. [27] investigated the stability and error analysis of a finite difference scheme using a uniform mesh and meshes graded in time. Liao ...
This paper uses the attached flow method for solving nonlinear second-order differential equations of the reaction–diffusion type. The key steps of the method consist of the following: (i) reducing the differentiability order by defining the first deriv
By multiplying the differential equation − Δ 2 ℵ i − 1 y = ϑ i ℵ i y −Δ2ℵ𝑖−1(𝔶)=𝜗𝑖ℵ𝑖(𝔶) by ℵ i y ℵ𝑖(𝔶) and utilizing Theorem 1, we obtain the following: ∑ i = 1 N | Δ ℵ i y | 2 = ϑ i ∑ i = 1 N ...
The perfect agreement of Equation (1) with the Monte Carlo results, for the whole evolution up to the detachment of all drug particles within the formulation, reveals that the bond cleavage chemical reaction, simulated as discussed above, exhibits first-order kinetics. Such first-order kinetics of...