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Mathematical modeling of landscape erosion :Convergence, singularities, and shocks in a continuous, transport-limited model.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Mathematical modeling of landscape erosion :
Reminder of title:	Convergence, singularities, and shocks in a continuous, transport-limited model.
Author:	Welsh, Edward Wilder.
Description:	102 p.
Notes:	Source: Dissertation Abstracts International, Volume: 64-08, Section: B, page: 3859.
Notes:	Supervisor: Andrea L. Bertozzi.
Contained By:	Dissertation Abstracts International64-08B.
Subject:	Mathematics.
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3102256
ISBN:	0496498266

Mathematical modeling of landscape erosion :Convergence, singularities, and shocks in a continuous, transport-limited model.
Welsh, Edward Wilder.

Mathematical modeling of landscape erosion :Convergence, singularities, and shocks in a continuous, transport-limited model. [electronic resource] - 102 p.

Source: Dissertation Abstracts International, Volume: 64-08, Section: B, page: 3859.

Thesis (Ph.D.)--Duke University, 2003.

This dissertation will examine continuous mathematical models of transport-limited landscape erosion. First, we will develop a coupled pair of partial differential equations describing landscape erosion: one equation will describe water evolution, and the second will describe evolution of the landscape. In subsequent chapters, we will investigate convergence, steady-state, and numerical approximation of solutions to the water equation, as well as stability of the coupled system. In the final chapter, we will find a class of nonphysical, unbounded solutions, suggest a remedy, and present two types of shocks found in this improved system. We will conclude by showing how these shocks first form a convex hillslope, and then transition to a mature, concave steady-state.

ISBN: 0496498266Subjects--Topical Terms:

184409
Mathematics.

Mathematical modeling of landscape erosion :Convergence, singularities, and shocks in a continuous, transport-limited model.
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500 $a Source: Dissertation Abstracts International, Volume: 64-08, Section: B, page: 3859.
500 $a Supervisor: Andrea L. Bertozzi.
502 $a Thesis (Ph.D.)--Duke University, 2003.
520 # $a This dissertation will examine continuous mathematical models of transport-limited landscape erosion. First, we will develop a coupled pair of partial differential equations describing landscape erosion: one equation will describe water evolution, and the second will describe evolution of the landscape. In subsequent chapters, we will investigate convergence, steady-state, and numerical approximation of solutions to the water equation, as well as stability of the coupled system. In the final chapter, we will find a class of nonphysical, unbounded solutions, suggest a remedy, and present two types of shocks found in this improved system. We will conclude by showing how these shocks first form a convex hillslope, and then transition to a mature, concave steady-state.
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