指数
非线性系统
临界指数
统计物理学
扩散
物理
数学
数学物理
数学分析
量子力学
相变
哲学
语言学
摘要
This paper is concerned with a cancer invasion model that incorporates porous medium diffusion (Δum) and extracellular matrix remodeling effects [ηω(1 − u − ω)] in a bounded domain of RN (N ≥ 2). Rich achievements have been achieved for the case η = 0 in the past ten years for the nonlinear diffusion case, but there is no any progress for η > 0. In this paper, we pay our attention to the global existence of solutions of the case η > 0, and establish the critical exponent m*=2N−2N of global solvability. More precisely, if m > m*, the solution will always exist globally, while if m < m*, there exist blow-up solutions. In this system, the remodeling effect of extracellular matrix [ηω(1 − u − ω)] bring some essential difficulties to the estimation of the haptotactic term, so the main technique we used is completely different from the case of η = 0.
科研通智能强力驱动
Strongly Powered by AbleSci AI