Mathematical Models for Erosion and the Optimal Transportation of Sediment
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Bjorn Birnir
Abstract
We investigate a mathematical theory for the erosion of sediment which begins with the study of a non-linear, parabolic, weighted 4-Laplace equation on a rectangular domain corresponding to a base segment of an extended landscape. Imposing natural boundary conditions, we show that the equation admits entropy solutions and prove regularity and uniqueness of weak solutions when they exist. We then investigate a particular class of weak solutions studied in previous work of the first author and produce numerical simulations of these solutions. After introducing an optimal transportation problem for the sediment flow, we show that this class of weak solutions implements the optimal transportation of the sediment.
©[2013] by Walter de Gruyter Berlin Boston
Articles in the same Issue
- Masthead
- Mathematical Models for Erosion and the Optimal Transportation of Sediment
- Comments on “He's Homotopy Perturbation Method for Calculating Adomian Polynomials”
- Biomechanical Analysis of Eyring Prandtl Fluid Model for Blood Flow in Stenosed Arteries
- Consensus Recovery from Intentional Attacks in Directed Nonlinear Multi-agent Systems
- Exp-function Method for Fractional Differential Equations
- Solving Nonlinear Problems with Singular Initial Conditions Using A Perturbed Scalar Homotopy Method
- Tri-integrable Couplings by Matrix Loop Algebras
- Extended Reductive Perturbation Method and Its Relation to the Re-normalization Method
- Neural Network Approaches to Data Fusion Calculation and Correction in Wireless Sensor Network – A Case Study Comparison between BPN, RBFN and GRNN
- A Catfish Effect Inspired Harmony Search Algorithm for Optimization
- An Exact, Fully Nonlinear Solution of the Poisson-Boltzmann Equation with Anti-symmetric Electric Potential Profiles
- Study on Nonlinear Oscillations of Gear Systems with Parametric Excitation Solved by Homotopy Analysis Method
Articles in the same Issue
- Masthead
- Mathematical Models for Erosion and the Optimal Transportation of Sediment
- Comments on “He's Homotopy Perturbation Method for Calculating Adomian Polynomials”
- Biomechanical Analysis of Eyring Prandtl Fluid Model for Blood Flow in Stenosed Arteries
- Consensus Recovery from Intentional Attacks in Directed Nonlinear Multi-agent Systems
- Exp-function Method for Fractional Differential Equations
- Solving Nonlinear Problems with Singular Initial Conditions Using A Perturbed Scalar Homotopy Method
- Tri-integrable Couplings by Matrix Loop Algebras
- Extended Reductive Perturbation Method and Its Relation to the Re-normalization Method
- Neural Network Approaches to Data Fusion Calculation and Correction in Wireless Sensor Network – A Case Study Comparison between BPN, RBFN and GRNN
- A Catfish Effect Inspired Harmony Search Algorithm for Optimization
- An Exact, Fully Nonlinear Solution of the Poisson-Boltzmann Equation with Anti-symmetric Electric Potential Profiles
- Study on Nonlinear Oscillations of Gear Systems with Parametric Excitation Solved by Homotopy Analysis Method
