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	A PARABOLIC SYSTEM WITH STRONG ABSORPTION MODELING DRY-LAND VEGETATION
	Ildefonso Diaz, Jesus; Hilhorst, Danielle; Kyriazopoulos, Paris
通讯作者	Diaz, JI (corresponding author), Univ Complutense Madrid, Inst Matemat Interdisciplinar, Plaza Ciencias 3, Madrid 28040, Spain.
来源期刊	ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS
ISSN	1072-6691
出版年	2021
英文摘要	We consider a variant of a nonlinear parabolic system, proposed by Gilad, von Hardenberg, Provenzale, Shachak and Meron, in desertification studies, in which there is a strong absorption. The system models the mutual interaction between the biomass, the soil-water content w and the surface-water height which is diffused by means of the degenerate operator Delta h(m) with m >= 2. The main novelty in this article is that the absorption is given in terms of an exponent a is an element of (0, 1), in contrast to the case alpha = 1 considered in the previous literature. Thanks to this, some new qualitative behavior of the dynamics of the solutions can be justified. After proving the existence of non-negative solutions for the system with Dirichlet and Neumann boundary conditions, we demonstrate the possible extinction in finite time and the finite speed of propagation for the surface-water height component h(t, x). Also, we prove, for the associate stationary problem, that if the precipitation datum p(x) grows near the boundary of the domain partial derivative Omega as d(x, partial derivative Omega)(2 alpha/m-alpha) then h(m) (x) grows, at most, as d(x, partial derivative Omega)(2/m-alpha). This property also implies the infinite waiting time property when the initial datum h(0)(x) grows at fast as d(x,partial derivative S(h(0)))(2m/m-alpha) near the boundary of its support S(h(0)).
英文关键词	Nonlinear parabolic system dry-land vegetation positive solution free boundary problem
类型	Article
语种	英语
收录类别	SCI-E
WOS记录号	WOS:000626729400001
WOS关键词	INTERFACES ; EXISTENCE
WOS类目	Mathematics, Applied ; Mathematics
WOS研究方向	Mathematics
资源类型	期刊论文
条目标识符	http://119.78.100.177/qdio/handle/2XILL650/350061
作者单位	[Ildefonso Diaz, Jesus] Univ Complutense Madrid, Inst Matemat Interdisciplinar, Plaza Ciencias 3, Madrid 28040, Spain; [Hilhorst, Danielle] Univ Paris Saclay, CNRS, F-91405 Orsay, France; [Hilhorst, Danielle] Univ Paris Saclay, Lab Math, F-91405 Orsay, France; [Kyriazopoulos, Paris] Univ Aegean, Dept Math, Samos 83200, Greece
推荐引用方式 GB/T 7714	Ildefonso Diaz, Jesus,Hilhorst, Danielle,Kyriazopoulos, Paris. A PARABOLIC SYSTEM WITH STRONG ABSORPTION MODELING DRY-LAND VEGETATION[J],2021.
APA	Ildefonso Diaz, Jesus,Hilhorst, Danielle,&Kyriazopoulos, Paris.(2021).A PARABOLIC SYSTEM WITH STRONG ABSORPTION MODELING DRY-LAND VEGETATION.ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS.
MLA	Ildefonso Diaz, Jesus,et al."A PARABOLIC SYSTEM WITH STRONG ABSORPTION MODELING DRY-LAND VEGETATION".ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS (2021).