학술논문
Global existence of classical solutions to a cross-diffusion predator-prey system with a free boundary.
Document Type
Journal
Author
Li, Chenglin (PRC-HHU-SM) AMS Author Profile
Source
Subject
35 Partial differential equations -- 35A General topics
35A09Classical solutions
92Biology and other natural sciences -- 92D Genetics and population dynamics
92D25Population dynamics
35A09
92
92D25
Language
English
Abstract
Summary: ``This paper is concerned with a cross-diffusion predator-prey system with a free boundary over a one-dimensional habitat. The free boundary shows the spreading front of the prey and predator which implies that the velocity of the expanding front is proportional to the gradients of the prey and predator. By the contraction mapping principle, $L^p$ estimates and Schauder estimates of parabolic equations, the local and global existence and uniqueness of classical solutions are established for this system.''