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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
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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). |
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