The Riemann Hilbert Problem for General Elliptic Complex Equations of Fourth Order

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二阶复椭圆Riemann—Hilbert边值问题

讨论了一般二阶非线性椭圆复方程的Riemann-Hilbert边值问题,首先给出Riemann-Hilbert问题及其适应性的概念,其次给出改进后的边值问题解的表述并证明了它的可解性,最后导出原Rremann-Hilbert边值问题的可解条件。     

The Discontinuous Riemann–Hilbert Problem for Elliptic Complex Equations of First Order

In this article, we first transform the general uniformly elliptic systems of first order equations with certain conditions into the complex equations, and propose the discontinuous Riemann- Hilbert problem and its modified well-posedness for the complex equations. Then we give a priori estimates of solutions of the modified discontinuous Riemann-Hilbert problem for the complex equations and verify its solvability. Finally the solvability results of the original discontinuous Riemann-Hilbert boundary value problem can be derived. The discontinuous boundary value problem possesses many applications in mechanics and physics etc.     

AN IRREGULAR OBLIQUE DERIVATIVE PROBLEM FOR SOME NONLINEAR ELLIPTIC EQUATIONS OF SECOND ORDER

1FormulationofirregularObliqueDerivativeProblemLetDbean(N 1)-connecteddomainwithboundaryr=UU=,r,6Cj(0相似文献   

二阶非线性椭圆型方程于无界域上的斜微商问题

在机械和物理中有许多问题的数学模型是一、二阶非线性椭圆型方程于包含无穷远点的多连通域上的某些边值问题，该文讨论了二阶非线性椭圆型方程于包含无穷远点的多连通域上的斜微商边值问题．     

Qualitative analysis of the invasion free boundary problem in biofilms

The work presents the qualitative analysis of the free boundary value problem related to the invasion model for multispecies biofilms. This model is based on the continuum approach for biofilm modeling and consists of a system of nonlinear hyperbolic partial differential equations for microbial species growth and spreading, a system of semilinear elliptic partial differential equations describing the substrate trends and a system of semilinear elliptic partial differential equations accounting for the diffusion and reaction of motile species within the biofilm. The free boundary evolution is regulated by a nonlinear ordinary differential equation. Overall, this leads to a free boundary value problem essentially hyperbolic. By using the method of characteristics, the partial differential equations constituting the invasion model are converted to Volterra integral equations. Then, the fixed point theorem is used for the uniqueness and existence result. The work is completed with numerical simulations describing the invasion of nitrite oxidizing bacteria in a biofilm initially constituted by ammonium oxidizing bacteria.     

Comparison theorem and uniqueness of positive solutions for sublinear elliptic equations

In semilinear elliptic equations, we prove that the necessary and sufficient condition for the comparison theorem of positive solutions to be valid is that the nonlinear term is sublinear. Our theorem needs neither any regularity of the nonlinear term nor the smoothness of the boundary. Applying this theorem, we prove the uniqueness of positive solutions for the Dirichlet problem. Received: 9 April 2008     

Symmetry results for overdetermined boundary value problems of nonlinear elliptic equations

We prove the radial symmetry of the solutions of second-order nonlinear elliptic equations for overdetermined Dirichlet and Neumann boundary value problems. In addition, a global uniqueness theorem of Holmgren type is given for nonlinear elliptic equations.     

Noncoercive Boundary Value Problems for Elliptic Partial Differential and Differential-Operator Equations

In this paper we find conditions guarantee that irregular boundary value problems for elliptic differential-operator equations of the second order in an interval are fredholm. We apply this result to find some algebraic conditions guarantee that irregular boundary value problems for elliptic partial differential equations of the second order in cylindrical domains are fredholm. Apparently this is the first paper where the regularity of an elliptic boundary value problem is not satisfied on a manifold of the dimension equal to dimension of the boundary. Nevertheless the problem is fredholm and the resolvent is compact. It is interesting to note that the considered boundary value problems for elliptic equations in a cylinder being with separating variables are noncoercive.     

多连通区域上一阶椭圆型复方程的Riemann-Hilbert问题与其适定性

In this article, we first propose the Riemann-Hilbert problem for uniformly elliptic complex equations of first order and its well-posed-ness in multiply connected domains.Then we give the integral representation of solutions for modified Riemann-Hilbert problem of the complex equations. Moreover we shall obtain a priori estimates of solutions of the modified Riemann-Hilbert problem and verify its solvability. Finally the solvability results of the original boundary value problem can be obtained.