A parabolic–hyperbolic system modeling the tumor growth with angiogenesis. (April 2022)

• Record Type: Journal Article
• Authors: Shen, Haishuang; Wei, Xuemei
• Is Part Of: Nonlinear analysis. Volume 64(2022)
• Publication Date: 2022-04
• Subjects: Parabolic–hyperbolic -- Angiogenesis -- Extracellular matrix -- Matrix degrading enzymes -- Nutrient; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2021.103456
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this paper, we study the parabolic–hyperbolic system about the growth of a tumor. The model is a coupled system of PDEs with Robin boundary, which involves nutrient density, extracellular matrix and matrix degrading enzyme. By transforming the free boundary into a fixed boundary and using strict mathematical analysis, we can prove the existence and uniqueness of the radially symmetric stationary solution. By the fixed point theorem, we obtain the existence and uniqueness of the radially symmetric solution globally in time.