Pointwise Gradient Estimates in Multi-dimensional Slow Diffusion Equations with a Singular Quenching Term

doi:10.1515/ans-2020-2076

	Pointwise Gradient Estimates in Multi-dimensional Slow Diffusion Equations with a Singular Quenching Term
	Nguyen Anh Dao2 ; Ildefonso Diaz, Jesus 1; Quan Ba Hong Nguyen 3
	2020-05
发表期刊	ADVANCED NONLINEAR STUDIES (IF:2.1[JCR-2023],1.8[5-Year])
ISSN	1536-1365
EISSN	2169-0375
卷号	20 期号:2 页码:477-502
发表状态	已发表
DOI	10.1515/ans-2020-2076
摘要	We consider the high-dimensional equation partial derivative(t)u -Delta u(m) + u(-beta)chi({u>0}) = 0, extending the mathematical treatment made in 1992 by B. Kawohl and R. Kersner for the one-dimensional case. Besides the existence of a very weak solution u is an element of C([0, T]; L-delta(1)(Omega)), with u(-beta)chi({u>0}) is an element of L-1 ((0, T) x Omega), delta(x) = d(x, partial derivative Omega), we prove some pointwise gradient estimates for a certain range of the dimension N, m >= 1 and beta is an element of (0, m), mainly when the absorption dominates over the diffusion (1 <= m < 2 + beta ). In particular, a new kind of universal gradient estimate is proved when m + beta <= 2. Several qualitative properties (such as the finite time quenching phenomena and the finite speed of propagation) and the study of the Cauchy problem are also considered.
关键词	Singular Absorption and Nonlinear Diffusion Equations Pointwise Gradient Estimates Quenching Phenomenon Free Boundary
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收录类别	SCI ; SCIE
语种	英语
资助项目	Ministerio de Ciencia, Innovacion y Universidades -Agencia Estatal de Investigacion (Spain)[MTM2017-85449-P]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000531060200014
出版者	WALTER DE GRUYTER GMBH
WOS关键词	SEMILINEAR ELLIPTIC-EQUATIONS ; PARABOLIC EQUATIONS ; LINEAR DIFFUSION ; EXISTENCE ; EXTINCTION ; DEPENDENCE ; CONVERGENCE ; REGULARITY ; BOUNDARY ; BEHAVIOR
原始文献类型	Article
引用统计	正在获取...
文献类型	期刊论文
条目标识符	https://kms.shanghaitech.edu.cn/handle/2MSLDSTB/120887
专题	数学科学研究所_PI研究组(P)_Dao Nguyen Anh组
通讯作者	Ildefonso Diaz, Jesus
作者单位	1.Univ Complutense Madrid, Inst Matemat Interdisciplinar, Madrid 28040, Spain 2.ShanghaiTech Univ, Inst Math Sci, Shanghai, Peoples R China 3.Univ Rennes 1, Inst Rech Math Rennes IRMAR, UFR Math, Rennes 35042, France
第一作者单位	数学科学研究所
第一作者的第一单位	数学科学研究所
推荐引用方式 GB/T 7714	Nguyen Anh Dao,Ildefonso Diaz, Jesus,Quan Ba Hong Nguyen. Pointwise Gradient Estimates in Multi-dimensional Slow Diffusion Equations with a Singular Quenching Term[J]. ADVANCED NONLINEAR STUDIES,2020,20(2):477-502.
APA	Nguyen Anh Dao,Ildefonso Diaz, Jesus,&Quan Ba Hong Nguyen.(2020).Pointwise Gradient Estimates in Multi-dimensional Slow Diffusion Equations with a Singular Quenching Term.ADVANCED NONLINEAR STUDIES,20(2),477-502.
MLA	Nguyen Anh Dao,et al."Pointwise Gradient Estimates in Multi-dimensional Slow Diffusion Equations with a Singular Quenching Term".ADVANCED NONLINEAR STUDIES 20.2(2020):477-502.