具间断系数的n维拟线性椭圆方程解的存在性

, PP. 53-56

Keywords: 拟线性椭圆方程,间断系数,存在性,挠射问题

Full-Text   Cite this paper   Add to My Lib

Abstract:

研究了具间断系数的n维拟线性椭圆方程.利用系数连续的方程逼近和估计,得到了解的存在性.

References

[1]	Verigin N N. Forcing of astringent solutions into mineral rocks with the aim of increasing the strength and water impermeability of the foundations of hydrotechnological structions[J]. Izv Akad Nauk SSSR Otd Tekh Nuak,1952,5:674-687.
[2]	Evans L C. A free boundary problem: The flow of two immiscible fluids in a one-dimmensional porous medium, I[J]. Indiana Univ Math J,1977,26:914-932.
[3]	Evans L C. A free boundary problem: The flow of two immiscible fluids in a one-dimensional porous medium, II[J]. Indiana Univ Math J,1978,27:93-111.
[4]	Liang J. The one-dimensional quasilinear verigin problem[J]. J Part Diff Eqns,1991,4:74-96.
[5]	Yi F H. Global classical solution of Muskat free boundary problem[J]. J Math Anal Appl,2003,288:442-461.
[6]	白东华,谭启建. 一类具两条自由边界的自由边值问题[J]. 四川大学学报:自然科学版,1993,30(2):154-163.
[7]	Kim K, Lin Z. A free boundary problem for a parabolic system describing an ecological model[J]. Nonlinear Anal: RWA,2009,10:428-436.
[8]	Kamynin L I. On the linear Verigin problem[J]. Dokl Akad Nauk SSSR,1963,150:1210-1213.
[9]	Kamynin L I. The method of heat potentials for a parabolic equation with discontinous coefficients[J]. Sibir Mate Z,1963,4:1071-1105.
[10]	Ladyzenskaya O A, Solonnikov V A, Ural’ceva N N. Linear and Quasilinear Equations of Parabolic Type[M]. Providence:Am Math Soc,1968.
[11]	Ladyzenskaya O A, Ural’ceva N N. Linear and Quasilinear Elliptic Equations[M]. New York:Academic Press,1968.
[12]	Ladyzenskaya O A, Ryvkind V Ja, Ural’ceva N N. Solvability of diffraction problems in the classical sense[J]. Trudy Mat Inst Steklov,1966,92:116-146.
[13]	兴梅. 间断系数的二阶椭圆型方程解的正则性[J]. 数学物理学报,2005,A25(5):685-693.
[14]	Tan Q J, Leng Z J. The regularity of the weak solutions for the ndimensional quasilinear elliptic equations with discontinuous coefficients[J]. J Math Res Exp,2008,28(4):779-788.
[15]	Tan Q J, Leng Z J. The regularity of generalized solutions for the ndimensional quasilinear parabolic diffraction problems[J]. Nonlinear Anal,2008,69:4624-4642.
[16]	Pao C V. Nonlinear Parabolic and Elliptic Equations[M]. New York:Plenum Press,1992:93-110.

Full-Text