检索结果-南通市图书馆

Acta Mathematica Sinica,English Series 2013年第9期29卷 1713-1722页

作者： Guo Chun WEN LMAM School of Mathematical Sciences Peking University

In this article, we first give the representation of solutions for the oblique derivative problem of mixed （Lavrentév-Bitsadze） equations in two connected domains, afterwards prove the uniqueness of solutions of the above problem. Moreover, we prove the solvability of oblique derivative problem for quasilinear mixed （Lavrentév-Bitsadze） equations of second order, and obtain a priori estimates of solutions of the above problem. The above problem is an open problem proposed by Rassias.

关键词： Existence and uniqueness oblique derivative problem Lavrentév-Bitsadze equations two connected domains

维普期刊数据库

oblique derivative problem for general Chaplygin-Rassias equations

在线全文

学校读者我要写书评

暂无评论

Science China Mathematics 2008年第1期51卷 5-36页

作者： WEN GuoChun LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, China LMAM School of Mathematical Sciences Peking University Beijing 100871 China

The present paper deals with the oblique derivative problem for general second order equations of mixed (elliptic-hyperbolic) type with the nonsmooth parabolic degenerate line $$K_1 (y)u_{xx} + \left| {K_2 (x)} \right|u_{yy} + a(x,y)u_x + b(x,y)u_y + c(x,y)u = - d(x,y)$$ in any plane domain D with the boundary ?D=Γ ∪ L 1 ∪ L 2 ∪ L 3 ∪ L 4, where Γ(? {y > 0}) ∈ C μ 2 (0 oblique derivative problemoblique derivative problem\frac{{\partial u}}{{\partial \nu }} = \fracoblique derivative problem{{H(x,y)}}\operatorname{Re} \left[ {\overline {\lambda (z)} u_{\tilde z} } \right] = r(z), z \in \Gamma \cup L_1 \cup L_4 , \operatorname{Im} \left[ {\overline {\lambda (z)} u_{\tilde z} } \right]\left| {_{z = z_l } } \right. = b_l ,l = 1,2, u( - 1) = b_0 ,u(1) = b_3 ,$$ in which z 1, z 2 are the intersection points of L 1, L 2, L 3, L 4 respectively. The above equations can be called the general Chaplygin-Rassias equations, which include the Chaplygin-Rassias equations $$K_1 (y)(M_2 (x)u_x )_x + M_1 (x)(K_2 (y)u_y )_y + r(x,y)u = f(x,y), in D$$ as their special case. The above boundary value problem includes the Tricomi problem of the Chaplygin equation: K(y)u xx+u yy = 0 with the boundary condition u(z) = ?(z) on Γ ∪ L 1 ∪ L 4 as a special case. Firstly some estimates and the existence of solutions of the corresponding boundary value problems for the degenerate elliptic and hyperbolic equations of second order are discussed. Secondly, the solvability of the Tricomi problem, the oblique derivative problem and Frankl problem for the general Chaplygin-Rassias equations are proved. The used method in this paper is different from those in other papers, because the new notations W(z) = W(x + iy) = $u_{\tilde z} $ = [H

关键词： oblique derivative problem equations of mixed type nonsmooth degenerate line 35J70 35L80 35N99

维普期刊数据库

The oblique derivative problem for nonlinear elliptic complex equations of second order in multiply connected unbounded domains

在线全文

学校读者我要写书评

暂无评论

Applied Mathematics(A Journal of Chinese Universities) 2013年第2期28卷 127-137页

作者： WEN Guo-chun LMAM School of Mathematical SciencesPeking University

In this article,we discuss that an oblique derivative boundary value problem for nonlinear uniformly elliptic complex equation of second order with the boundary conditions in a multiply connected unbounded domain *** above boundary value problem will be called problem *** certain conditions,by using the priori estimates of solutions and Leray-Schauder fixed point theorem,we can obtain some results of the solvability for the above boundary value problem（0.1） and（0.2）.

关键词： oblique derivative problem nonlinear elliptic complex equation multiply connected unboundeddomain.

维普期刊数据库

THE oblique derivative BOUNDARY VALUE problem FOR ELLIPTIC COMPLEX EQUATIONS OF FOURTH ORDER

在线全文

学校读者我要写书评

暂无评论

河北省科学院学报 1997年第3期 2-8页

作者：杨广武许克明闻国椿

ＴＨＥＯＢＬＩＱＵＥＤＥＲＩＶＡＴＩＶＥＢＯＵＮＤＡＲＹＶＡＬＵＥＰＲＯＢＬＥＭＦＯＲＥＬＬＩＰＴＩＣＣＯＭＰＬＥＸＥＱＵＡＴＩＯＮＳＯＦＦＯＵＲＴＨＯＲＤＥＲＹａｎｇＧｕａｎｇｗｕＸｕＫｅｍｉｎｇ（杨广武）（许克明... 详细信息

ＴＨＥＯＢＬＩＱＵＥＤＥＲＩＶＡＴＩＶＥＢＯＵＮＤＡＲＹＶＡＬＵＥＰＲＯＢＬＥＭＦＯＲＥＬＬＩＰＴＩＣＣＯＭＰＬＥＸＥＱＵＡＴＩＯＮＳＯＦＦＯＵＲＴＨＯＲＤＥＲＹａｎｇＧｕａｎｇｗｕＸｕＫｅｍｉｎｇ（杨广武）（许克明）（ＨｅｂｅｉＵｎｉｖｅｒｓｉｔｙ...

关键词： Elliptic complex equation oblique derivative problem A priori estimate

Quasilinear equations of mixed type (Ⅰ )——oblique derivative problems

在线全文

同方期刊数据库

学校读者我要写书评

暂无评论

Progress in Natural Science:Materials International 1999年第2期 9-16页

作者：闻国椿田茂英 Beijing 100871 China Department of Mathematics Peking University

The oblique derivative boundary value problem for quasitinear second-order equations of mixed ( el liptic-hyperbolic) type is studied. Firstly the representation of solutions of the above boundary value problem, is given, and then the uniqueness and existence of solutions of the above problem are proved In the meantime a priori estimates of solutions for the problem are obtained.

关键词： oblique derivative problem quasilinear equations of mixed type.

Integral Equation Method for Inverse Scattering problem from the Far-Field Data

在线全文

同方期刊数据库

学校读者我要写书评

暂无评论

Advances in Applied Mathematics and Mechanics 2021年第6期13卷 1558-1574页

作者： Yuqing Hu School of Science Jinling Institute of TechnologyNanjingJiangsu 211169China

Consider the inverse scattering problem in terms of Helmholtz *** study a simply connected domain with oblique derivative boundary *** the case of constant l,given a finite number of incident wave,the shape of the scatterer is reconstructed from the measured far-field *** propose a Newton method which is based on the nonlinear boundary integral *** computing the Fr´echet derivatives with respect to the unknown boundary,the nonlinear equation is transformed to its linear form,then we show the iteration scheme for the inverse *** conclude our paper by presenting several numerical examples for shape reconstruction to show the validity of the method we presented.

关键词： Helmholtz equation oblique derivative problem nonlinear integral equation iterative solution numerics.

A new approach to quasilinear equations of mixed type in general domains

维普期刊数据库评论

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Progress in Natural Science:Materials International 1999年第8期 21-27页

作者：闻国椿 Beijing 100871 China Department of Mathematics Peking University

The oblique derivative boundary value problem for quasilinear second order equations of mixed (elliptic-hyperbolic) type in general domains is considered. Using a new method, the unique solvability of the above bounda... 详细信息

关键词： oblique derivative problem equations of mixed type general domains.