关于含小参数的拟线性椭圆型方程的狄立克雷问题
On the Dirichlet Problem for a Quasilinear Elliptic Equation with a Small Parameter
-
摘要: 本文研究最高阶导数项含小参数的拟线性椭圆型方程的狄立克雷问题,在退化方程的特征是曲线和区域是凸域的一般情形下,给出构造一致有效渐近解的方法,并证明当小参数是充分小时,狄立克雷问题的解是存在和唯一.Abstract: The method of "boundary layer corrections" is developed to study the Dirichlet problem for a quasilinear elliptic equation in a bounded domain, when the degenerate equation has characteristics tangent to the boundary. The existence and uniqueness of solution have been proved. The uniformly valid asymptotic expansion of solution has been constructed.
-
[1] Berger,M.S.and Fraenkel,L.E.,On the asymptotic solution of a nonlinear Dirichlet problem,J.Math,Mech 19(7),(1973),553-585. [2] Fife,P.C.,Semilinear elliptic boundary value problems with small parameters,Arch.Rat.Mech.and Anal.,52(2),(1973),205-232. [3] Roberts,P.H.,Singularities of Hartmann layers,Proc.Royal Soc.,Ser.A,300(1967),94-107. [4] Grasman,J.,On the birth of boundary layers,Math.Centre Tracts,36,Amsterdam,(1971). [5] Van Harten,A.J.,Nonlinear singular perturbation problems:Proofs of correctness of a formal approximation based on a contraction principle in a Banach space,J.Math.Anal,and Appl.,65(1),(1978),126-168. [6] Holland,C.J.,Singular perturbations in elliptic boundary value problems,J,Diff.Equ.,20(1),(1976),248-265. [7] Howes,F.A.Singularly perturbed semilinear elliptic boundary value problems,Comm.Partial Diff.Equ.,4(1),(1979),1-39. [8] Леликова,Е.Ф.,Об асимптоуике решения эллиптнческого уравявния второг порядка с малым пзрамбтром при старших цроизводпых,Дцфф.Урав.,12(10)(1976).1852-1865. [9] Ильин,А.М.,Калашников,А.С.,Олейнык,О.А.,Линсйиые уравнення второго поряка параболического типа,17,5(105),(1962),3-146. [10] Ладыженская,О.А.,Уральцева,Н.Н.,Линейные ы Квазилинейные Уравнення Эллыптнческоо Типа,Изд""Наука"",Москва(1964).
点击查看大图
计量
- 文章访问数: 1526
- HTML全文浏览量: 51
- PDF下载量: 540
- 被引次数: 0