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Báo cáo hóa học: " Blow-up for an evolution p-laplace system with nonlocal sources and inner absorptions"

Tuyển tập các báo cáo nghiên cứu về hóa học được đăng trên tạp chí hóa hoc quốc tế đề tài : Blow-up for an evolution p-laplace system with nonlocal sources and inner absorptions | Zhang et al. Boundary Value Problems 2011 2011 29 http www.boundaryvalueproblems.eom content 2011 1 29 o Boundary Value Problems a SpringerOpen Journal RESEARCH Open Access Blow-up for an evolution p-laplace system with nonlocal sources and inner absorptions Yan Zhang1 Dengming Liu2 Chunlai Mu2 and Pan Zheng2 Correspondence liudengming08@163.com 2College of Mathematics and Statistics Chongqing University Chongqing 410031 PR China Full list of author information is available at the end of the article Springer Abstract This paper investigates the blow-up properties of positive solutions to the following system of evolution p-Laplace equations with nonlocal sources and inner absorptions ut - div Vu p-2Vu fn vmdx - aur x e ft t 0 vt - div Vvlq-2Vv fữ undx - pVs x e t 0 with homogeneous Dirichlet boundary conditions in a smooth bounded domain o e Rn N 1 where p q 2 m n r s 1 a b 0. Under appropriate hypotheses the authors discuss the global existence and blow-up of positive weak solutions by using a comparison principle. 2010 Mathematics Subject Classification 35B35 35K60 35K65 35K57. Keywords evolution p-Laplace system global existence blow-up nonlocal sources absorptions 1 Introduction In this paper we deal with the blow-up properties of positive solutions to an evolution Ji-Laplace system of the form ut - div Vu p-2 Vu fa vmdx - aur x e A t 0 vt - div Vvb-2Vv undx - pvs x e . t 0 u x t v x t 0 x e d t 0 u x 0 u0 x v x 0 v0 x x e 1.1 where p q 2 m n r s 1 a b 0 o is a bounded domain in R N 1 with a smooth boundary dif the initial data u0 x e C A w0 p v0fxi e C Q A w . ii and u x 0 Ff 0 where v denotes the unit outer nor-0 dv dv mal vector on dii. System 1.1 is the classical reaction-diffusion system of Fujita-type for p q 2. If p 2 q 2 1.1 appears in the theory of non-Newtonian fluids 1 2 and in nonlinear filtration theory 3 . In the non-Newtonian fluids theory the pair p q is a characteristic quantity of the medium. Media with p q 2 2 are called dilatant fluids and .