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Virtual Element Method for Control Constrained Dirichlet Boundary Control Problem Governed by the Diffusion Problem
This article develops a conforming virtual element method for a control-constrained Dirichlet boundary optimal control problem governed by the...
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Fitted Difference Scheme on a Non-uniform Mesh for Singularly Perturbed Parabolic Reaction–Diffusion with Large Negative Shift and Non-local Boundary Condition
In this paper, we study the numerical solution of singularly perturbed parabolic reaction–diffusion problems with large delay in space, and the right...
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Numerical Treatment for a Coupled System of Singularly Perturbed Reaction–Diffusion Equations with Robin Boundary Conditions and Having Boundary and Interior Layers
A system of \(k(\ge 2)\) linear singularly perturbed...
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Rate of convergence for reaction–diffusion equations with nonlinear Neumann boundary conditions and \({\mathcal {C}}^1\) variation of the domain
In this paper, we propose the compact convergence approach to deal with the continuity of attractors of some reaction–diffusion equations under...
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Accurate Boundary Treatment for Riesz Space Fractional Diffusion Equations
We consider numerical boundary treatment for solving the Cauchy problems of the Riesz space fractional diffusion equation with compact initial data...
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Global Renormalised Solutions and Equilibration of Reaction–Diffusion Systems with Nonlinear Diffusion
The global existence of renormalised solutions and convergence to equilibrium for reaction–diffusion systems with nonlinear diffusion are...
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Fractional Anomalous Diffusion
In this chapter, we discuss the general problem of fractional diffusion equationFractional diffusion equation in connection with the anomalous...
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A non-uniform Haar wavelet method for a singularly perturbed convection–diffusion type problem with integral boundary condition on an exponentially graded mesh
In this article, we present a numerical approach based on non-uniform Haar wavelets on an exponentially graded mesh to approximate the solution of a...
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Exact rate of accelerated propagation in the Fisher-KPP equation with nonlocal diffusion and free boundaries
Accelerated propagation is a new phenomenon associated with nonlocal diffusion problems. In this paper, we determine the exact rate of accelerated...
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Implicit interpolation method for immersed boundary methods
Immersed boundary (IB) methods have been successfully implemented for different applications. This paper focuses on the immersed boundary...
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Threshold Dynamics for Infection Age-Structured Epidemic Models with Spatial Diffusion and Degenerate Diffusion
This paper is devoted to studying the threshold dynamics for infection age-structured epidemic models with non-degenerate diffusion and degenerate...
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Economic Growth and Pollution Diffusion
As an additional application of the methods presented in this volume, in this chapter, we introduce an environmental issue concerning the control of...
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Global dynamics for an SVEIR epidemic model with diffusion and nonlinear incidence rate
In this paper, we investigate an SVEIR epidemic model with reaction–diffusion and nonlinear incidence. We establish the well-posedness of the...
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Hopf Bifurcation Analysis of a Predator–Prey Model with Prey Refuge and Fear Effect Under Non-diffusion and Diffusion
In this paper, we propose a predator–prey model with prey refuge and fear effect under non-diffusion and diffusion. For the non-diffusion ODE model,...
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Analysis of a Full Discretization for a Fractional/Normal Diffusion Equation with Rough Dirichlet Boundary Data
This paper considers a fully discrete approximation of a fractional/normal diffusion equation with rough Dirichlet boundary data. The approximation...
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Numerical solution of two-dimensional inverse time-fractional diffusion problem with non-local boundary condition using a-polynomials
In this paper, we obtain the numerical solution of two-dimensional inverse time-fractional diffusion problem with non-local boundary condition using a ...
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Stability analysis of a second-order difference scheme for the time-fractional mixed sub-diffusion and diffusion-wave equation
This study investigates a class of initial-boundary value problems pertaining to the time-fractional mixed sub-diffusion and diffusion-wave equation...
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Convergence to Sharp Traveling Waves of Solutions for Burgers-Fisher-KPP Equations with Degenerate Diffusion
This paper is concerned with the convergence to sharp traveling waves of solutions with semi-compactly supported initial data for Burgers-Fisher-KPP...
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Controlled Diffusion Processes
InDiffusion process the remainder of these notes we consider a class of $$\mathbb...
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Aggregation Kinetics in Sedimentation: Effect of Diffusion of Particles
AbstractThe aggregation kinetics of settling particles is studied theoretically and numerically using the advection–diffusion equation. Agglomeration...
