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Global existence for a haptotaxis model of cancer invasion with tissue remodeling

Authors
Journal
Nonlinear Analysis Real World Applications
1468-1218
Publisher
Elsevier
Publication Date
Volume
12
Issue
1
Identifiers
DOI: 10.1016/j.nonrwa.2010.06.027
Keywords
  • Haptotaxis Model
  • Cancer Invasion
  • Tissue Remodeling
  • Global Existence
  • A Priori Estimates
Disciplines
  • Biology
  • Mathematics

Abstract

Abstract This paper considers a 3×3 haptotaxis model of cancer invasion with tissue remodeling. The model consists of a parabolic haptotaxis partial differential equation (PDE) describing the evolution of tumor cell density, an ordinary differential equation modeling the proteolysis and the remodeling of the extracellular matrix (ECM), and a parabolic PDE governing the evolution of the matrix degrading enzyme (MDE) concentration. In addition to random diffusion, tumor cells are biased towards higher ECM density, which is referred to as haptotaxis. Under a restrictive assumption on the coefficients, the global existence and uniqueness of classical solutions to the model in two dimensions, along with the boundedness of solutions in two and three dimensions, is proved by establishing some delicate a priori estimates.

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