共查询到20条相似文献,搜索用时 15 毫秒
1.
《Nonlinear Analysis: Theory, Methods & Applications》2009,70(12):4550-4566
We investigate the homogeneous Dirichlet boundary value problem for a class of second-order nonlinear elliptic partial differential equations with a gradient term and singular data. Under general conditions on the data, we study the behaviour of the solution near the boundary of the domain. Under suitable additional conditions we also investigate the second-order term in the asymptotic expansion of the solution in terms of the distance from the boundary. 相似文献
2.
The authors investigate the problem of identifying the domainG of a harmonic functionu such that Cauchy data are given on a known portion of the boundary ofG, while a zero Dirichlet condition is specified on the remaining portion of the boundary, which is to be found. Under certain conditions on the domainG, it is shown that the problem reduces to identifying the coefficients of an elliptic equation which, in turn, is converted into the problem of minimizing a functional. Under certain conditions onG, it is shown that the solution, if it exists, is unique. An application is pointed out for the problem of designing a vessel shape that realizes a given plasma shape.This work was completed with a financial support from the National Basic Research in the Natural Sciences. 相似文献
3.
Zhonghai Xu Zhenguo FengJiashan Zheng 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(1):1-8
The Keldysh equation is a more general form of the classic Tricomi equation from fluid dynamics. Its well-posedness and the regularity of its solution are interesting and important. The Keldysh equation is elliptic in y>0 and is degenerate at the line y=0 in R2. Adding a special nonlinear absorption term, we study a nonlinear degenerate elliptic equation with mixed boundary conditions in a piecewise smooth domain—similar to the potential fluid shock reflection problem. By means of an elliptic regularization technique, a delicate a priori estimate and compact argument, we show that the solution of a mixed boundary value problem of the Keldysh equation is smooth in the interior and Lipschitz continuous up to the degenerate boundary under some conditions. We believe that this kind of regularity result for the solution will be rather useful. 相似文献
4.
We obtain estimates on the continuous dependence on the coefficient for second-order non-linear degenerate Neumann type boundary value problems. Our results extend previous work of Cockburn et al., Jakobsen and Karlsen, and Gripenberg to problems with more general boundary conditions and domains. A new feature here is that we account for the dependence on the boundary conditions. As one application of our continuous dependence results, we derive for the first time the rate of convergence for the vanishing viscosity method for such problems. We also derive new explicit continuous dependence on the coefficients results for problems involving Bellman-Isaacs equations and certain quasilinear equation. 相似文献
5.
Boundary regularity for nonlinear elliptic systems 总被引:3,自引:0,他引:3
J.F. Grotowski 《Calculus of Variations and Partial Differential Equations》2002,15(3):353-388
We consider questions of boundary regularity for solutions of certain systems of second-order nonlinear elliptic equations.
We obtain a general criterion for a weak solution to be regular in the neighbourhood of a given boundary point. The proof
yields directly the optimal regularity for the solution in this neighbourhood. This result is new for the situation under
consideration (general nonlinear second order systems in divergence form, with inhomogeneity obeying the natural growth conditions).
Received: 6 July 2001 / Accepted: 27 September 2001 / Published online: 28 February 2002 相似文献
6.
We investigate the existence of a global classical solution to the generalized Goursat problem. Under some degenerate assumptions of boundary conditions, we prove that the solution approaches a combination of Lipschitz continuous and a piecewise C1 traveling wave solution. 相似文献
7.
MoJIAQI 《高校应用数学学报(英文版)》1996,11(2):153-158
Abstract. The singularly perturbed problems for elliptic systems in unbounded domains are considered. Under suitable conditions and by using the comparison theorem the existence and asymptotic behavior of solution for the boundary value problems studied, 相似文献
8.
We deal with the time-dependent Navier–Stokes equations (NSE) with Dirichlet boundary conditions on the whole domain or, on a part of the domain and open boundary conditions on the other part. It is shown numerically that combining the penalty-projection method with spatial discretization by the Marker And Cell scheme (MAC) yields reasonably good results for solving the above-mentioned problem. The scheme which has been introduced combines the backward difference formula of second-order (BDF2, namely Gear’s scheme) for the temporal approximation, the second-order Richardson extrapolation for the nonlinear term, and the penalty-projection to split the velocity and pressure unknowns. Similarly to the results obtained for other projection methods, we estimate the errors for the velocity and pressure in adequate norms via the energy method. 相似文献
9.
Ilaria Fragalà 《Journal of Differential Equations》2008,245(5):1299-1322
We consider semilinear elliptic Dirichlet problems in bounded domains, overdetermined with a Neumann condition on a proper part of the boundary. Under different kinds of assumptions, we show that these problems admit a solution only if the domain is a ball. When these assumptions are not fulfilled, we discuss possible counterexamples to symmetry. We also consider Neumann problems overdetermined with a Dirichlet condition on a proper part of the boundary, and the case of partially overdetermined problems on exterior domains. 相似文献
10.
We study a class of optimization dynamics problems related to investment under uncertainty. The general model problem is
reformulated in terms of an obstacle problem associated to a second-order elliptic operator which is not in divergence form.
The spatial domain is unbounded and no boundary conditions are a priori specified. By using the special structure of the differential
operator and the spatial domain, and some approximating arguments, we show the existence and uniqueness of a solution of the
problem. We also study the regularity of the solution and give some estimates on the location of the coincidence set. 相似文献
11.
《Applied Mathematics and Optimization》2008,45(3):251-267
We study a class of optimization dynamics problems related to investment under uncertainty. The general model problem is
reformulated in terms of an obstacle problem associated to a second-order elliptic operator which is not in divergence form.
The spatial domain is unbounded and no boundary conditions are a priori specified. By using the special structure of the differential
operator and the spatial domain, and some approximating arguments, we show the existence and uniqueness of a solution of the
problem. We also study the regularity of the solution and give some estimates on the location of the coincidence set. 相似文献
12.
13.
L.E. Payne 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(4):971-1014
This paper deals with the blow-up of the solution to a semilinear second-order parabolic equation with nonlinear boundary conditions. It is shown that under certain conditions on the nonlinearities and data, blow-up will occur at some finite time and when blow-up does occur upper and lower bounds for the blow-up time are obtained. 相似文献
14.
Peng ZhouJie Bao Zhigui Lin 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(7):2523-2533
This paper is concerned with a double fronts free boundary problem for the heat equation with a localized nonlinear reaction term. The local existence and uniqueness of the solution are given by applying the contraction mapping theorem. Then we present some conditions so that the solution blows up in finite time. Finally, the long-time behavior of the global solution is discussed. We show that the solution is global and fast if the initial data is small and that a global slow solution is possible when the initial data is suitably large. 相似文献
15.
Zai-yun Zhang Zhen-hai Liu Yue-zhong Chen 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(6):1878-1889
In this paper, we investigate the stabilization of heat flow with boundary time-varying delay effect. Under some assumptions, we prove exponential stability of the solution applying variable norm technique and modified Lyapunov functional approach. 相似文献
16.
In this paper we prove the optimal boundary regularity under natural structural conditions for a large class of nonlinear elliptic equations with singular terms near the boundary. By a careful construction of super- and sub-solutions, we obtain precise growth estimates for solutions at the boundary and reduce the boundary regularity to the interior one by a rescaling argument. 相似文献
17.
Klaus Deckelnick Hans-Christoph Grunau 《Calculus of Variations and Partial Differential Equations》2007,30(3):293-314
The one-dimensional Willmore equation is studied under Navier as well as under Dirichlet boundary conditions. We are interested
in smooth graph solutions, since for suitable boundary data, we expect the stable solutions to be among these. In the first
part, classical symmetric solutions for symmetric boundary data are studied and closed expressions are deduced. In the Navier
case, one has existence of precisely two solutions for boundary data below a suitable threshold, precisely one solution on
the threshold and no solution beyond the threshold. This effect reflects that we have a bending point in the corresponding
bifurcation diagram and is not due to that we restrict ourselves to graphs. Under Dirichlet boundary conditions we always have existence of precisely one
symmetric solution. In the second part, we consider boundary value problems with nonsymmetric data. Solutions are constructed
by rotating and rescaling suitable parts of the graph of an explicit symmetric solution. One basic observation for the symmetric
case can already be found in Euler’s work. It is one goal of the present paper to make Euler’s observation more accessible
and to develop it under the point of view of boundary value problems. Moreover, general existence results are proved. 相似文献
18.
Qinian Jin Aobing Li YanYan Li 《Calculus of Variations and Partial Differential Equations》2007,28(4):509-543
In this paper we consider a fully nonlinear version of the Yamabe problem on compact Riemannian manifold with boundary. Under
various conditions we derive local estimates for solutions and establish some existence results.
Partially supported by NSF grant DMS-0401118. 相似文献
19.
In this paper, we investigate the existence of positive solutions for singular elliptic equations with mixed Dirichlet‐Neumann boundary conditions involving Sobolev‐Hardy critical exponents and Hardy terms by using the concentration compactness principle, the strong maximum principle and the Mountain Pass lemma. We also prove, under complementary conditions, that there is no nontrivial solution if the domain is star‐shaped with respect to the origin. 相似文献
20.
Veli Shakhmurov 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(8):2383-2397
This paper focuses on nonlocal boundary value problems for linear and nonlinear abstract elliptic equations in Banach spaces. Here equations and boundary conditions contain certain parameters. The uniform separability of the linear problem and the existence and uniqueness of maximal regular solution of nonlinear problem are obtained in Lp spaces. For linear case the discreteness of spectrum of corresponding parameter dependent differential operator is obtained. The behavior of solution when the parameter approaches zero and its smoothness with respect to the parameter is established. Moreover, we show the estimate for analytic semigroups in terms of interpolation spaces. This fact can be used to obtain maximal regularity properties for abstract boundary value problems. 相似文献