共查询到20条相似文献,搜索用时 591 毫秒
1.
N. Mavinga 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(15):5171-5188
We study the existence of (generalized) bounded solutions existing for all times for nonlinear parabolic equations with nonlinear boundary conditions on a domain that is bounded in space and unbounded in time (the entire real line). We give a counterexample which shows that a (weak) maximum principle does not hold in general for linear problems defined on the entire real line in time. We consider a boundedness condition at minus infinity to establish (one-sided) L∞-a priori estimates for solutions to linear boundary value problems and derive a weak maximum principle which is valid on the entire real line in time. We then take up the case of nonlinear problems with (possibly) nonlinear boundary conditions. By using comparison techniques, some (delicate) a priori estimates obtained herein, and nonlinear approximation methods, we prove the existence and, in some instances, positivity and uniqueness of strong full bounded solutions existing for all times. 相似文献
2.
Tadeusz Jankowski 《Applied mathematics and computation》2010,216(4):1242-1249
We investigate the existence of solutions to nonlinear first-order difference problems with advanced arguments. Sufficient conditions when such problems have solutions (extremal or unique) are given. Linear advanced difference inequalities are also discussed. According to my knowledge, it is a first paper when a monotone iterative method is applied to nonlinear boundary value problems for first-order difference equations with advanced arguments. An example illustrates the theoretical results. 相似文献
3.
E. V. Yushkov 《Differential Equations》2012,48(9):1212-1218
We use the nonlinear capacity method to prove the blow-up of solutions of initial-boundary value problems of hydrodynamic type in bounded domains. We present sufficient boundary conditions ensuring the blow-up of the solution of an equation that is globally solvable under the classical boundary conditions. We estimate the blow-up time of solutions under given initial conditions. Note that it is the first result concerning blow-up for one of the problems considered. 相似文献
4.
T. Jankowski 《Journal of Optimization Theory and Applications》2010,144(1):56-68
We apply the monotone iterative method to nonlinear four-point boundary conditions for differential–algebraic systems with
causal operators. Sufficient conditions under which such problems have solutions (extremal or unique) are given. An example
illustrates the theoretical results. 相似文献
5.
S. M. Chuiko 《Ukrainian Mathematical Journal》2009,61(4):657-673
We investigate the problem of the determination of conditions for the existence of solutions of weakly nonlinear Noetherian
boundary-value problems for systems of ordinary differential equations and the construction of these solutions. We consider
the special critical case where the equation for finding the generating solution of a weakly nonlinear Noetherian boundary-value
problem turns into an identity. We improve the classification of critical cases and construct an iterative algorithm for finding
solutions of weakly nonlinear Noetherian boundary-value problems in the special critical case. 相似文献
6.
We investigate local convergence of the Lagrange-Newton method for nonlinear optimal control problems subject to control constraints including the situation where the terminal state is fixed. Sufficient conditions for local quadratic convergence of the method based on stability results for the solutions of nonlinear control problems are discussed. 相似文献
7.
关于非线性波动方程的爆破现象 总被引:4,自引:0,他引:4
通过引入一类“爆破因子K(u,ut)”,讨论了非线性波动方程分别具Newmann边界条件和Dirichlet边界条件时,混合问题对于常见的各种非线性情形及初值条件,解在有限时间内的爆破行为。 相似文献
8.
ONINITIAL BOUNDARYVALUEPROBLEMSFORNONLINEARSCHRDINGEREQUATIONS¥LiYongsheng(李用声)ChenQingyi(陈庆益)(Dept.ofMath.,HuazhongUnv.ofSci... 相似文献
9.
On a new analytical method for flow between two inclined walls 总被引:1,自引:0,他引:1
Efficient analytical methods for solving highly nonlinear boundary value problems are rare in nonlinear mechanics. The purpose of this study is to introduce a new algorithm that leads to exact analytical solutions of nonlinear boundary value problems and performs more efficiently compared to other semi-analytical techniques currently in use. The classical two-dimensional flow problem into or out of a wedge-shaped channel is used as a numerical example for testing the new method. Numerical comparisons with other analytical methods of solution such as the Adomian decomposition method (ADM) and the improved homotopy analysis method (IHAM) are carried out to verify and validate the accuracy of the method. We show further that with a slight modification, the algorithm can, under certain conditions, give better performance with enhanced accuracy and faster convergence. 相似文献
10.
E. I. Galakhov 《Proceedings of the Steklov Institute of Mathematics》2008,260(1):112-122
We prove the nonexistence of solutions for some nonlinear ordinary differential equations and inequalities, for quasilinear partial differential equations and inequalities in bounded domains with singular points on the boundary, and for systems of such equations and inequalities. The proofs are based on the method of nonlinear capacity. We also give examples demonstrating that the conditions obtained are sharp in the class of problems under consideration. 相似文献
11.
We investigate a semi-smooth Newton method for the numerical solution of optimal control problems subject to differential-algebraic
equations (DAEs) and mixed control-state constraints. The necessary conditions are stated in terms of a local minimum principle.
By use of the Fischer-Burmeister function the local minimum principle is transformed into an equivalent nonlinear and semi-smooth
equation in appropriate Banach spaces. This nonlinear and semi-smooth equation is solved by a semi-smooth Newton method. We
extend known local and global convergence results for ODE optimal control problems to the DAE optimal control problems under
consideration. Special emphasis is laid on the calculation of Newton steps which are given by a linear DAE boundary value
problem. Regularity conditions which ensure the existence of solutions are provided. A regularization strategy for inconsistent
boundary value problems is suggested. Numerical illustrations for the optimal control of a pendulum and for the optimal control
of discretized Navier-Stokes equations conclude the article. 相似文献
12.
近来非局部问题的研究日见增多,但涉及带非线性边界条件的初值问题文献 较少.本文目的在于证明一个半线性方程的齐次边值问题和一个非线性边界条件问题 解的存在性.主要使用半群,分数次幂函数空间,广义Poincare算子等工具. 相似文献
13.
Tadeusz Jankowski 《Applied mathematics and computation》2011,218(6):2549-2557
By using the monotone iterative method, some new results are established for nonlinear boundary conditions of difference problems with causal operators. We formulate sufficient conditions under which such problems have extremal solutions. Difference inequalities with causal operators are also discussed. Two examples are added to illustrate the results. 相似文献
14.
《Journal of Computational and Applied Mathematics》1997,84(2):189-206
The paper deals with parabolic differential-functional equations. Initial-boundary value problems are considered with impulses given in fixed points. We prove theorems on difference-functional impulsive inequalities generated by original problems.Explicit finite difference schemes are used to approximate the solutions of the original problems. We give sufficient conditions for the convergence of sequences of approximate solutions under the assumptions that the right-hand sides satisfy the nonlinear estimates of the Perron type with respect to the functional argument. In proof of the convergence of difference methods we apply theorems on difference-functional impulsive inequalities. 相似文献
15.
16.
The main purpose of this paper is the existence of solutions and controllability for semilinear boundary problems with nonlocal initial conditions. We show that the solutions are given by a variation of constants formula which allows us to study the exact controllability for this kind of problems with control and nonlinear terms at the boundary. The included application to a size structured population equation provides a motivation for abstract results. 相似文献
17.
E. V. Yushkov 《Theoretical and Mathematical Physics》2012,172(1):932-938
We investigate the nonlinear third-order differential equation (uxx ? u)t + u xxx + uux = 0 describing the processes in semiconductors with a strong spatial dispersion. We study the problem of the existence of global solutions and obtain sufficient conditions for the absence of global solutions for some initial boundary value problems corresponding to this equation. We consider examples of solution blowup for initial boundary value and Cauchy problems. We use the Mitidieri-Pokhozhaev nonlinear capacity method. 相似文献
18.
In this paper, we consider the existence of solutions for a class of nonlinear impulsive problems with Dirichlet boundary conditions. We obtain some new existence theorems of solutions for the nonlinear impulsive problem by using critical point theory. We extend and improve some recent results. 相似文献
19.
Lingchen Kong Levent Tunçel Naihua Xiu 《Journal of Optimization Theory and Applications》2012,153(2):357-376
We consider existence and uniqueness properties of a solution to homogeneous cone complementarity problem. Employing an algebraic
characterization of homogeneous cones due to Vinberg from the 1960s, we generalize the properties of existence and uniqueness
of solutions for a nonlinear function associated with the standard nonlinear complementarity problem to the setting of homogeneous
cone complementarity problem. We provide sufficient conditions for a continuous function so that the associated homogeneous
cone complementarity problems have solutions. In particular, we give sufficient conditions for a monotone continuous function
so that the associated homogeneous cone complementarity problem has a unique solution (if any). Moreover, we establish a global
error bound for the homogeneous cone complementarity problem under some conditions. 相似文献
20.
M. Bogoya R. Ferreira J.D. Rossi 《Journal of Mathematical Analysis and Applications》2008,337(2):1284-1294
We deal with boundary value problems (prescribing Dirichlet or Neumann boundary conditions) for a nonlocal nonlinear diffusion operator which is analogous to the porous medium equation. First, we prove existence, uniqueness and the validity of a comparison principle for these problems. Next, we impose boundary data that blow up in finite time and study the behavior of the solutions. 相似文献