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Existence of weak solutions to a system of nonlinear partial differential equations modelling ice streams

Authors
Journal
Nonlinear Analysis Real World Applications
1468-1218
Publisher
Elsevier
Publication Date
Volume
8
Issue
1
Identifiers
DOI: 10.1016/j.nonrwa.2005.07.003
Keywords
  • Ice Sheet Models
  • Nonlinear Partial Differential Equations System Of Mixed Type
  • Free Boundaries
Disciplines
  • Mathematics

Abstract

Abstract This paper deals with the mathematical analysis of a nonlinear system of three differential equations of mixed type. It describes the generation of fast ice streams in ice sheets flowing along soft and deformable beds. The system involves a nonlinear parabolic PDE with a multivalued term in order to deal properly with a free boundary which is naturally associated to the problem of determining the basal water flux in a drainage system. The other two equations in the system are an ODE with a nonlocal (integral) term for the ice thickness, which accounts for mass conservation and a first order PDE describing the ice velocity of the system. We first consider an iterative decoupling procedure to the system equations to obtain the existence and uniqueness of solutions for the uncoupled problems. Then we prove the convergence of the iterative decoupling scheme to a bounded weak solution for the original system.

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