共查询到20条相似文献,搜索用时 15 毫秒
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G. D. Orudzhev 《Ukrainian Mathematical Journal》1993,45(3):471-474
Polynomial approximations are constructed for the solutions of differential equations of the first and second order in a Banach space for which the Cauchy problem is stated correctly.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 3, pp. 440–442, March, 1993. 相似文献
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Raad Noori Butris 《Ukrainian Mathematical Journal》1991,43(9):1174-1177
Numerical-analytic methods are considered for the investigation of the existence and the approximate construction of periodic solutions of nonlinear differential-operator equations, subjected to an impulse action.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 9, pp. 1260–1264, September, 1991. 相似文献
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Antoine Delcroix Victor Dévoué 《Journal of Mathematical Analysis and Applications》2009,353(1):386-403
We discuss various methods of regularization of singular differential problems. Their common point is that we use the flexibility of the theories of nonlinear generalized functions for adapting the regularization to the singularity of the problem. We particularly underline the relationship between the generalized solutions and those classical or distribution, when they exist, giving a general result for the case of the regularization of data. 相似文献
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We study spherically symmetric solutions of the Vlasov-Poisson system in the context of algebras of generalized functions. This allows to model highly concentrated initial configurations and provides a consistent setting for studying singular limits of the system. The proof of unique solvability in our approach depends on new stability properties of the system with respect to perturbations. 相似文献
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We obtained decay and growth estimates for solutions of second-order and third-order differential-operator equations in a Hilbert space. Applications to initial–boundary value problems for linear and nonlinear non-stationary partial differential equations modeling the strongly damped nonlinear improved Boussinesq equation, the dual-phase-lag heat conduction equations, the equation describing wave propagation in relaxing media, and the Moore–Gibson–Thompson equation are given. 相似文献
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Ruth F. Curtain 《Journal of Mathematical Analysis and Applications》1977,60(3):570-595
Existence and uniqueness theorems are proved for a general class of stochastic linear abstract evolution equations, with a general type of stochastic forcing term. The abstract evolution equation is modeled using an evolution operator (or 2-parameter semigroup) approach and this includes linear partial differential equations and linear differential delay equations. The stochastic forcing term is modeled by defining an Itô stochastic integral with respect to a Hilbert space-valued orthogonal increments process, which can be used to model both Gaussian and non-Gaussian white noise processes. The theory is illustrated by examples of stochastic partial differential equations and delay equations, which arise in filtering problems for distributed and delay systems. 相似文献
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Hideshi Yamane 《Proceedings of the American Mathematical Society》2007,135(11):3659-3667
We construct solutions to nonlinear wave equations that are singular along a prescribed noncharacteristic hypersurface, which is the graph of a function satisfying not the Eikonal but another partial differential equation of the first order. The method of Fuchsian reduction is employed.
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Dongho Chae Peter Constantin Diego Córdoba Francisco Gancedo Jiahong Wu 《纯数学与应用数学通讯》2012,65(8):1037-1066
This paper establishes several existence and uniqueness results for two families of active scalar equations with velocity fields determined by the scalars through very singular integrals. The first family is a generalized surface quasigeostrophic (SQG) equation with the velocity field u related to the scalar θ by $u=\nabla^\perp\Lambda^{\beta-2}\theta$ , where $1<\beta\le 2$ and $\Lambda=(-\Delta)^{1/2}$ is the Zygmund operator. The borderline case β = 1 corresponds to the SQG equation and the situation is more singular for β > 1. We obtain the local existence and uniqueness of classical solutions, the global existence of weak solutions, and the local existence of patch‐type solutions. The second family is a dissipative active scalar equation with $u=\nabla^\perp (\log(I-\Delta))^\mu\theta\ {\rm for}\ \mu>0$ , which is at least logarithmically more singular than the velocity in the first family. We prove that this family with any fractional dissipation possesses a unique local smooth solution for any given smooth data. This result for the second family constitutes a first step towards resolving the global regularity issue recently proposed by K. Ohkitani. © 2012 Wiley Periodicals, Inc. 相似文献
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M. Guerra 《Journal of Mathematical Sciences》2009,156(3):440-567
This text presents a complete theory of existence/uniqueness and the structure of generalized solutions for singular linear-quadratic
optimal control problems. Generalized optimal controls are distributions of order r and the corresponding generalized trajectories are distributions of order (r − 1). r is the “order of singularity” of the problem, an integer no greater than the dimension of the state space. Its value is obtained
through a certain reduction procedure. In the final section, some perspectives and partial results concerning the extension
of these results to nonlinear problems are briefly discussed.
Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions),
Vol. 27, Optimal Control, 2007. 相似文献
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Carlos Cueto Camejo Robin Gröpler Gerald Warnecke 《Mathematical Methods in the Applied Sciences》2015,38(11):2171-2184
In this article, we prove the existence of solutions to the coagulation equation with singular kernels. We use weighted L1‐spaces to deal with the singularities in order to obtain regular solutions. The Smoluchowski kernel is covered by our proof. The weak L1 compactness methods are applied to suitably chosen approximating equations as a base of our proof. A more restrictive uniqueness result is also mentioned. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
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Daniel Cobb 《Journal of Differential Equations》1982,46(3):310-323
Equations of the form E? = Ax + u, with E and A square matrices and E singular, are considered. The controversy that exists in the literature concerning the solutions of such equations is investigated. Solutions are arrived at through an application of singular perturbation theory. 相似文献