Lattice fractional diffusion equation of random order
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DOI: 10.1002/mma.3644
Abstract: The discrete fractional calculus is used to fractionalize difference equations. Simulations of the fractional logistic map unravel that the chaotic solution is conveniently obtained. Then a Riesz fractional difference is defined for fractional partial difference… read more here.
Keywords: fractional diffusion; equation random; lattice fractional; random order ... See more keywords
A singular reaction-diffusion equation associated with brain lactate kinetics
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DOI: 10.1002/mma.4150
Abstract: Our aim in this paper is to study the well-posedness of a singular reaction-diffusion equation which is related with brain lactate kinetics, when spatial diffusion is taken into account. Copyright © 2016 John Wiley &… read more here.
Keywords: diffusion; brain lactate; singular reaction; reaction diffusion ... See more keywords
The Crank‐Nicolson/interpolating stabilized element‐free Galerkin method to investigate the fractional Galilei invariant advection‐diffusion equation
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DOI: 10.1002/mma.5871
Abstract: Recently, finding a stable and convergent numerical procedure to simulate the fractional partial differential equations (PDEs) is one of the interesting topics. Meanwhile, the fractional advection‐diffusion equation is a challenge model numerically and analytically. This… read more here.
Keywords: advection diffusion; diffusion equation; fractional galilei;
On a final value problem for fractional reaction‐diffusion equation with Riemann‐Liouville fractional derivative
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DOI: 10.1002/mma.6103
Abstract: In this paper, we study a backward problem for a fractional diffusion equation with nonlinear source in a bounded domain. By applying the properties of Mittag‐Leffler functions and Banach fixed point theorem, we establish some… read more here.
Keywords: problem fractional; diffusion equation; problem; final value ... See more keywords
New idea of Atangana‐Baleanu time‐fractional derivative to advection‐diffusion equation
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DOI: 10.1002/mma.6123
Abstract: The analytical study of one‐dimensional generalized fractional advection‐diffusion equation with a time‐dependent concentration source on the boundary is carried out. The generalization consists into considering the advection‐diffusion equation with memory based on the time‐fractional Atangana‐Baleanu… read more here.
Keywords: advection diffusion; diffusion equation; atangana baleanu; diffusion ... See more keywords
Asymptotic analysis of an advection‐diffusion equation involving interacting boundary and internal layers
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DOI: 10.1002/mma.6425
Abstract: As ε goes to zero, the unique solution of the scalar advection‐diffusion equation ytε−εyxxε+Myxε=0 , (x,t)∈(0,1)×(0,T) with Dirichlet boundary conditions exhibits a boundary layer of size O(ε) and an internal layer of size O(ε) .… read more here.
Keywords: advection diffusion; diffusion equation; asymptotic analysis;
Data completion problem for the advection‐diffusion equation with aquifer point sources
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DOI: 10.1002/mma.6868
Abstract: We consider the inverse problem of recovering the missing flux and concentration on some part of a boundary of an aquifer using overspecified measurements available on some accessible part. The aquifer is under the action… read more here.
Keywords: advection diffusion; point; diffusion equation; problem ... See more keywords
Three regularization methods for identifying the initial value of homogeneous anomalous secondary diffusion equation
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DOI: 10.1002/mma.7654
Abstract: In this paper, the inverse problem of initial value identification for homogeneous anomalous diffusion equation with Riemann‐Liouville fractional derivative in time is studied. We prove that this kind of problem is ill‐posed. We analyze the… read more here.
Keywords: problem; homogeneous anomalous; initial value; diffusion equation ... See more keywords
Blow-Up Phenomenon for a Reaction–Diffusion Equation with Weighted Nonlocal Gradient Absorption Terms
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DOI: 10.1007/s00009-021-01795-5
Abstract: This paper deals with the blow-up phenomenon of solutions to a reaction–diffusion equation with weighted nonlocal gradient absorption terms in a bounded domain. Based on the method of auxiliary function and the technique of modified… read more here.
Keywords: reaction diffusion; equation weighted; blow phenomenon; nonlocal gradient ... See more keywords
A Nonlinear Diffusion Equation-Based Model for Ultrasound Speckle Noise Removal
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DOI: 10.1007/s00332-017-9414-1
Abstract: Ultrasound images are contaminated by speckle noise, which brings difficulties in further image analysis and clinical diagnosis. In this paper, we address this problem in the view of nonlinear diffusion equation theories. We develop a… read more here.
Keywords: diffusion; speckle noise; diffusion equation; model ... See more keywords
Exact Solutions in Optimal Design Problems for Stationary Diffusion Equation
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DOI: 10.1007/s10440-018-0204-z
Abstract: We consider two-phase multiple state optimal design problems for stationary diffusion equation. Both phases are taken to be isotropic, and the goal is to find the optimal distribution of materials within domain, with prescribed amounts,… read more here.
Keywords: problems stationary; stationary diffusion; diffusion equation; optimal design ... See more keywords