Search
Search Results
-
Interface development for the nonlinear degenerate multidimensional reaction–diffusion equations II: fast diffusion versus absorption
This paper presents a full classification of the short-time behavior of the solution and the interfaces in the Cauchy problem for the nonlinear...
-
Diffusion
A common example of diffusion is given by the heat conduction in a solid body. Conduction comes from molecular collision, transferring heat by...
-
Uniformly Convergent Numerical Scheme for Solving Singularly Perturbed Parabolic Convection-Diffusion Equations with Integral Boundary Condition
The singularly perturbed parabolic convection-diffusion equations with integral boundary conditions and a large negative shift are studied in this...
-
Fitted operator method for parabolic singularly perturbed convection-diffusion problems via polynomial cubic spline
This article introduces a new fitted operator method for singularly perturbed parabolic convection-diffusion having right boundary layer. We...
-
Nonlocal Turbulent Diffusion Models
A brief review of the emergence and development of the nonlocal approach to the problem of turbulent diffusion with a discussion of the physical...
-
Arbitrary Lagrangian–Eulerian Local Discontinuous Galerkin Method for Linear Convection–Diffusion Equations
In this paper, we present and analyze an arbitrary Lagrangian–Eulerian local discontinuous Galerkin (ALE-LDG) method for one-dimensional linear...
-
Boundary Exponential Stabilization for a Class of Coupled Reaction-Diffusion Equations with State Delay
A class of coupled parabolic PDEs with time delay is considered. We treat the problem of boundary exponential stabilization where the goal is to...
-
High-Order Numerical Method for Solving a Space Distributed-Order Time-Fractional Diffusion Equation
This article proposes a high-order numerical method for a space distributed-order time-fractional diffusion equation. First, we use the mid-point...
-
Topological sensitivity method for reconstruction of the spatial component in the source term of a time-fractional diffusion equation
In the paper, an inverse source problem for a time-fractional diffusion equation is formulated and proved. The topological sensitivity analysis...
-
The Finite-Time Blow-Up for Semilinear Fractional Diffusion Equations with Time \(\psi \)-Caputo Derivative
This article deals with a semilinear time-space fractional diffusion equation and a coupled semilinear diffusion system of two time-space fractional...
-
Fractional Stefan Problem: A Survey of the Recent Results
AbstractThe paper presents a survey of the recent fractional generalizations of the Stefan problem. This free boundary value problem in the classical...
-
Modelling the reduction of quartz in a quartz–carbon pellet
Traditional refining of silicon generates carbon dioxide emissions that are released into the atmosphere. An alternative process under experimental...
-
Visualizing Fluid Flows via Regularized Optimal Mass Transport with Applications to Neuroscience
The regularized optimal mass transport (rOMT) problem adds a diffusion term to the continuity equation in the original dynamic formulation of the...
-
Well-posedness and asynchronous exponential growth of an age-weighted structured fish population model with diffusion in \(L^1\)
In the present paper, we address the asymptotic behavior of a fish population system structured in age and weight, while also incorporating spatial...
-
Numerical Method for a Boundary Value Problem for a Linear System of Partially Singularly Perturbed Parabolic Delay Differential Equations of Reaction-Diffusion Type
The problem of a partially singularly perturbed boundary value problem for a linear system of reaction-diffusion type parabolic second-order delay...
-
Multiscale simulation of colloids ingressing porous layers with evolving internal structure
We report on a reaction-diffusion model posed on multiple spatial scales that accounts for diffusion, aggregation, fragmentation, and deposition of...
-
Mixing Local and Nonlocal Evolution Equations
In this paper, we study the homogenization of a stochastic process and its associated evolution equations in which we mix a local part (given by a...