文献详情
A parabolic-hyperbolic system modeling the growth of a tumor
文献类型：期刊
通讯作者：Li, R (reprint author), Renmin Univ China, Sch Math, Beijing 100872, Peoples R China.
期刊名称：JOURNAL OF DIFFERENTIAL EQUATIONS影响因子和分区
年：2019
卷：267
期：2
页码：693-741
ISSN：0022-0396
关键词：Free boundary; Shooting method; Singular integro-differential equations; Uniqueness; Simulation
摘要：In this paper, we consider a model with tumor microenvironment involving nutrient density, extracellular matrix and matrix degrading enzymes, which satisfy a coupled system of PDEs with a free boundary. For this coupled parabolic-hyperbolic free boundary problem, we prove that there is a unique radially symmetric solution globally in time. The stationary problem involves an ODE system which is transformed into a singular integro-differential equation. We establish a well-posed theorem for such g ...More
In this paper, we consider a model with tumor microenvironment involving nutrient density, extracellular matrix and matrix degrading enzymes, which satisfy a coupled system of PDEs with a free boundary. For this coupled parabolic-hyperbolic free boundary problem, we prove that there is a unique radially symmetric solution globally in time. The stationary problem involves an ODE system which is transformed into a singular integro-differential equation. We establish a well-posed theorem for such general types of equations by the shooting method; the theorem is then applied to our problem for the existence of a stationary solution. In addition, for this highly nonlinear problem, we also prove the uniqueness of the stationary solution, which is a nontrivial result. Moreover, numerical simulations indicate that the stationary solution is likely locally asymptotically stable for reasonable range of parameters. (c) 2019 Elsevier Inc. All rights reserved. ...Hide

DOI：10.1016/j.jde.2019.01.020
百度学术：A parabolic-hyperbolic system modeling the growth of a tumor
语言：外文
基金：China Scholarship CouncilChina Scholarship Council
作者其他论文



CRISPR/Cas9-Mediated SlNPR1 mutagenesis reduces tomato plant drought tolerance.Li, Rui, Liu, Chunxue, Zhao, Ruirui, et al. .BMC PLANT BIOLOGY. 2019, 19.
Melatonin Induces Disease Resistance to Botrytis cinerea in Tomato Fruit by Activating Jasmonic Acid Signaling Pathway.Liu, Chunxue, Chen, Lingling, Zhao, Ruirui, et al. .JOURNAL OF AGRICULTURAL AND FOOD CHEMISTRY. 2019, 67(22), 6116-6124.
Enhanced Ion Conduction via Epitaxially Polymerized Two-Dimensional Conducting Polymer for High-Performance Cathode in Zinc-Ion Batteries.Zang, Xiaoling, Wang, Xusheng, Liu, Haili, et al. .ACS APPLIED MATERIALS & INTERFACES. 2020, 12(8), 9347-9354.
Knockout of SlMAPK3 enhances tolerance to heat stress involving ROS homeostasis in tomato plants.Yu, Wenqing, Wang, Liu, Zhao, Ruirui, et al. .BMC PLANT BIOLOGY. 2019, 19(1).
ABA signaling rather than ABA metabolism is involved in trehalose-induced drought tolerance in tomato plants.Yu, Wenqing, Zhao, Ruirui, Wang, Liu, et al. .PLANTA. 2019, 250(2), 643-655.