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On algebraically stabilized schemes for convection–diffusion–reaction problems
An abstract framework is developed that enables the analysis of algebraically stabilized discretizations in a unified way. This framework is applied...
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Speed Selection of Traveling Waves of a Reaction–Diffusion–Advection Equation with High-Order Terms
In this paper, we investigate the speed selection mechanism of traveling wave solutions for a reaction–diffusion–advection equation with high-order...
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Spreading Speeds of Time-Dependent Partially Degenerate Reaction-Diffusion Systems
This paper is concerned with the spreading speeds of time dependent partially degenerate reaction-diffusion systems with monostable nonlinearity. By...
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Reduced Basis Approach for Convection-Diffusion Equations with Non-linear Boundary Reaction Conditions
This paper aims at an efficient strategy to solve drift-diffusion problems with non-linear boundary conditions as they appear, e.g., in heterogeneous...
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A SUPG formulation augmented with shock-capturing for solving convection-dominated reaction–convection–diffusion equations
In this computational study, stabilized finite element solutions of convection-dominated stationary and linear reaction–convection–diffusion...
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Discontinuous Galerkin Method Based on the Reduced Space for the Nonlinear Convection–Diffusion–Reaction Equation
In this paper, by introducing a reconstruction operator based on the Legendre moments, we construct a reduced discontinuous Galerkin (RDG) space that...
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Oscillatory Motions of Multiple Spikes in Three-Component Reaction–Diffusion Systems
For three specific singular perturbed three-component reaction–diffusion systems that admit N -spike solutions in one of the components on a finite...
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Global ML Stability of the Delayed Fractional-Order Coupled Reaction-Diffusion System on Networks without Strong Connectedness
This chapter primarily focuses on examining the existence of solutions and the global Mittag-Leffler stability in delayed fractional-order coupled...
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On the Limit of Solutions for a Reaction–Diffusion Equation Containing Fractional Laplacians
A kind of nonlocal reaction-diffusion equations on an unbounded domain containing a fractional Laplacian operator is analyzed. To be precise, we...
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An orthogonal spline collocation method for singularly perturbed parabolic reaction–diffusion problems with time delay
In this article, a numerical technique is developed and analyzed for singularly perturbed delay parabolic reaction–diffusion problems with Dirichlet...
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Gaussian belief propagation for transient reaction–diffusion problems
Reaction–diffusion problems are found in several fields, such as fluid dynamics, heat transfer and electromagnetism. An accurate and efficient...
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Virtual element method for the quasilinear convection-diffusion-reaction equation on polygonal meshes
In this paper, we analyze the virtual element method for the quasilinear convection-diffusion-reaction equation. The most important part in the...
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Invariant subspace method and exact solutions of the coupled system of time-fractional convection–reaction–diffusion equations
In this paper, we present how to apply the invariant subspace method for finding the linear invariant product spaces and exact solutions of the...
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Dynamics of a reaction–diffusion dengue fever model with incubation periods and vertical transmission in heterogeneous environments
In this paper, we incorporate incubation periods of dengue virus, vertical transmission of dengue virus and climate factors into the spread of dengue...
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Exponential input-to-state stabilization of stochastic nonlinear reaction–diffusion systems with time-varying delays and exogenous disturbances via boundary control
The boundary stabilization problem of stochastic nonlinear reaction–diffusion systems (SNRDSs) with time-varying delay, exogenous disturbance, and...
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A class of fractional parabolic reaction–diffusion systems with control of total mass: theory and numerics
In this paper, we prove global-in-time existence of strong solutions to a class of fractional parabolic reaction–diffusion systems posed in a bounded...
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Numerical Solution of Reaction–Diffusion Equations with Convergence Analysis
In this manuscript, we implement a spectral collocation method to find the solution of the reaction–diffusion equation with some initial and boundary...
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Discretised Flux Balance Analysis for Reaction–Diffusion Simulation of Single-Cell Metabolism
Metabolites have to diffuse within the sub-cellular compartments they occupy to specific locations where enzymes are, so reactions could occur....
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Propagation Dynamics for Time–Space Periodic and Partially Degenerate Reaction–Diffusion Systems with Time Delay
This paper is concerned with the propagation dynamics of a large class of time–space periodic and partially degenerate reaction–diffusion systems...
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A posteriori error estimates for the time-dependent Navier-Stokes system coupled with the convection-diffusion-reaction equation
In this paper we study the a posteriori error estimates for the time dependent Navier-Stokes system coupled with the convection-diffusion-reaction...