共查询到20条相似文献,搜索用时 15 毫秒
1.
Kewei Zhang 《Calculus of Variations and Partial Differential Equations》2006,26(2):171-199
We establish the existence of infinitely many weak solutions for the the one-dimensional version of the well-known and widely
used Perona-Malik anisotropic diffusion equation model in image processing. We establish the existence result under the homogeneous
Neumann condition with smooth non-constant initial values. Our method is to convert the problem into a partial differential
inclusion problem. 相似文献
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This paper is devoted to Young measure solutions of a class of forward-backward diffusion equations. Inspired by the idea from a recent work of Demoulini, we first discuss the regular case by introducing the Young measure solutions and prove the existence for such solutions, and then approximate the extreme case by the approach of regularization and establish the existence of Young measure solutions in the class of functions with bounded variation. 相似文献
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Norbert Christopeit 《Stochastic Processes and their Applications》1984,17(1):137-146
For a certain class of stochastic differential equations with nonlinear drift and degenerate diffusion term existence of a weak solution is shown. 相似文献
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We apply a variational approach to the one-dimensional version of the widely used Perona-Malik equation in image processing. We rephrase the problem into the one related to the quasiconvex hull of a graph in the space of 2×2 matrices M2×2. We then use the solutions of some heat equations as the centre of the mass for the Young measure-valued solutions to construct the approximate solutions by using simple laminates. The approximate solutions can be viewed as solutions of a perturbation problem by W−1,p (or W−1,∞) functions. The sequences of the approximate solutions generates Young measure-valued solutions. Our results also show that the solutions of the one-dimensional Perona-Malik equation are unstable under small W−1,∞ perturbations. 相似文献
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Kamel Al-Khaled Mohamed Ali Hajji 《Journal of Mathematical Analysis and Applications》2008,344(2):1165-1175
The objectives of this paper are twofold. Firstly, to prove the existence of an approximate solution in the mean for some nonlinear differential equations, we also investigate the behavior of the class of solutions which may be associated with the differential equation. Secondly, we aim to implement the homotopy perturbation method (HPM) to find analytic solutions for strongly nonlinear differential equations. 相似文献
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《Stochastics An International Journal of Probability and Stochastic Processes》2013,85(3-4):133-150
This paper concerns the existence of control functions such that a system of controlled stochastic differential equations (SDE) with periodic coefficients has a solution which is periodic in distribution. We show that bounded periodic controls acting in the same direction as the Driving Wiener process will achieve this under some nondegeneracy condition on the diffusion part. The main tool is an approximation theorem for solutions of SDEs which enables one to check certain stability conditions on a more suitable differential equation 相似文献
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In this paper, by using Kranoselskii fixed point point theorem and Mawhin''s continuation theorem, we establish two existence theorem on the periodic solutions for a class of three-order neutral differential equations. 相似文献
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Criteria are established for existence of multiple positive solutions to the boundary value problems expressed by second-order delay differential equations of the form
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We study the existence of positive solutions for the following boundary value problem on infinite interval for second-order functional differential equations:
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This paper is concerned with periodic solutions of first-order nonlinear functional differential equations with deviating
arguments. Some new sufficient conditions for the existence of periodic solutions are obtained. The paper extends and improves
some well-known results. 相似文献
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Zhaoxia Liu 《Journal of Mathematical Analysis and Applications》2011,382(2):731-747
In this paper, we consider the elliptic system of two equations in H1(RN)×H1(RN):
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Gabriele Bonanno Roberto Livrea 《Journal of Mathematical Analysis and Applications》2010,363(2):627-638
Under an appropriate oscillating behavior of the nonlinear term, the existence of infinitely many periodic solutions for a class of second order Hamiltonian systems is established. Moreover, the existence of two non-trivial periodic solutions for Hamiltonian systems with not coercive potential is obtained, and the existence of three periodic solutions for Hamiltonian systems with coercive potential is pointed out. The approach is based on critical point theorems. 相似文献
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In this paper, the global existence of solutions to the initial boundary value problem for a class of quasi-linear wave equations with viscous damping and source terms is studied by using a combination of Galerkin approximations, compactness, and monotonicity methods. 相似文献