Abstract
In this paper, we consider a gradient-driven mathematical model of antiangiogenesis in tumor growth. In the model, the movement of endothelial cells is governed by diffusion of themselves and chemotaxis in response to gradients of tumor angiogenic factors and angiostatin. The concentration of tumor angiogenic factors and angiostatin is assumed to diffuse and decay. The resulting system consists of three parabolic partial differential equations. In the present paper, we study the global existence and boundedness of classical solutions of the system under homogeneous Neumann boundary conditions.
Highlights
Angiogenesis is a crucial step in the metastatic cascade of solid tumors growth
X ∈ (0, L) and (0, L) is the interval in which the blood vessel and the secondary tumor are located. e endothelial cell receptors become desensitized to high concentration of tumor angiogenic factors as assumed in [4]; we take the chemotactic function
We consider a gradient-driven mathematical model of angiogenic response of endothelial cells to a secondary tumor proposed by Anderson et al in [4]. e model consists of three semilinear parabolic PDEs and assumes that the endothelial cells respond chemotactically to two opposing chemical gradients: a gradient of tumor angiogenic factor and a gradient of angiostatin. e blood vessel is usually very long
Summary
Angiogenesis is a crucial step in the metastatic cascade of solid tumors growth During this process, besides tumor angiogenic factors, a primary tumor secretes substances (angiostatin [1] and endostatin [2]) to inhibit the formation of a vasculature around the secondary tumors [1, 3]. E endothelial cell receptors become desensitized to high concentration of tumor angiogenic factors as assumed in [4]; we take the chemotactic function. Wei and Cui [6] prove the existence and uniqueness of global classical solution for system (3). Erefore, as a first step, we shall study the global existence and boundedness of (3)–(5) solutions for the problem (3)–(5) under the assumptions (6)–(8).
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