共查询到20条相似文献,搜索用时 0 毫秒
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V. G. Romanov 《Journal of Applied and Industrial Mathematics》2018,12(3):531-539
Under consideration is the problem of continuation of the wave field from the boundary of a half-plane inside it. We obtain stability estimate for the solution of the corresponding Cauchy problem. 相似文献
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V. G. Romanov 《Siberian Mathematical Journal》2005,46(5):925-934
We consider the linear wave equation in a domain of the x, t-space bounded from above and below by some smooth surfaces and from the sides by a cylindrical surface with generator parallel to the t-axis. We study the Cauchy problem for this equation with data on a piece of the timelike cylindrical surface and establish a stability estimate for a solution to the problem. 相似文献
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Romanov V. G. Bugueva T. V. Dedok V. A. 《Journal of Applied and Industrial Mathematics》2021,15(1):118-128
Journal of Applied and Industrial Mathematics - Given a hyperbolic equation with variable coefficients, we construct a regularizing algorithm to solve the problem of continuation of the wave field... 相似文献
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V. G. Romanov T. V. Bugueva V. A. Dedok 《Journal of Applied and Industrial Mathematics》2018,12(4):716-728
Some regularization algorithm is proposed related to the problem of continuation of the wave field from the planar boundary into the half-plane. We consider a hyperbolic equation whose main part coincideswith the wave operator, whereas the lowest term contains a coefficient depending on the two spatial variables. The regularization algorithm is based on the quasi-reversibility method proposed by Lattes and Lions. We consider the solution of an auxiliary regularizing equation with a small parameter; the existence, the uniqueness, and the stability of the solution in the Cauchy data are proved. The convergence is substantiated of this solution to the exact solution as the small parameter vanishes. A solution of an auxiliary problem is constructed with the Cauchy data having some error. It is proved that, for a suitable choice of a small parameter, the approximate solution converges to the exact solution. 相似文献
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This study considers the robust identification of the parameters describing a Sugeno type fuzzy inference system with uncertain data. The objective is to minimize the worst-case residual error using a numerically efficient algorithm. The Sugeno type fuzzy systems are linear in consequent parameters but nonlinear in antecedent parameters. The robust consequent parameters identification problem can be formulated as second-order cone programming problem. The optimal solution of this second-order cone problem can be interpreted as solution of a Tikhonov regularization problem with a special choice of regularization parameter which is optimal for robustness (Ghaoui and Lebret (1997). SAIM Journal of Matrix Analysis and Applications 18, 1035–1064). The final regularized nonlinear optimization problem allowing simultaneous identification of antecedent and consequent parameters is solved iteratively using a generalized Gauss–Newton like method. To illustrate the approach, several simulation studies on numerical examples including the modelling of a spectral data function (one-dimensional benchmark example) is provided. The proposed robust fuzzy identification scheme has been applied to approximate the physical fitness of patients with a fuzzy expert system. The identified fuzzy expert system is shown to be capable of capturing the decisions (experiences) of a medical expert. 相似文献
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We consider the Cauchy problem for dynamic Lame systems in the cylinder GT = D × (0,T) constructed over a domain D in a three-dimensional space, where the initial data are given in some strip in the lateral surface of the cylinder. The strip has the form S × (0,T), where S is an open subset of the boundary surface of the domain D. This problem is ill-posed. Under certain requirements to the configuration of S, we derive an explicit formula for solutions to this problem.
相似文献7.
Yunyun Ma & Fuming Ma 《数学研究通讯:英文版》2012,28(4):300-312
In this paper, we consider the reconstruction of the wave field in a
bounded domain. By choosing a special family of functions, the Cauchy problem
can be transformed into a Fourier moment problem. This problem is ill-posed. We
propose a regularization method for obtaining an approximate solution to the wave
field on the unspecified boundary. We also give the convergence analysis and error
estimate of the numerical algorithm. Finally, we present some numerical examples to
show the effectiveness of this method. 相似文献
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Regular solutions to second-order elliptic systems on the plane are representable in terms of A-analytic functions satisfying an operator equation of the Beltrami type. We prove Carleman-type formulas for reconstruction of solutions from data on a part of the boundary of the domain. We use these formulas for solving the Cauchy problems for the system of Lame equations, the Navier–Stokes system, and the system of equations of elasticity with resilience. 相似文献
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K. Burrage J. van Casteren S. Piskarev 《Numerical Functional Analysis & Optimization》2013,34(10):1019-1040
We consider a stochastic regularization method for solving the backward Cauchy problem in Banach spaces. An order of convergence is obtained on sourcewise representative elements. 相似文献
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高德智 《应用泛函分析学报》2004,6(1):48-51
利用自反Banach空间中弱紧算子的因子分解技巧,对于一类非齐次项具有连续Lipschitz扰动的柯西问题,当其齐次项算子生成强连续算子半群且具有紧豫解式限制时,证明了方程强解的存在性. 相似文献
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Differential Equations - In a finite-dimensional Hilbert space, we consider the Cauchy problem for a second-order integro-differential evolution equation with memory where the integrand is the... 相似文献
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V. Varlamov 《Mathematical Methods in the Applied Sciences》1996,19(8):639-649
We consider the Cauchy problem for the damped Boussinesq equation governing long wave propagation in a viscous fluid of small depth. For the cases of one, two, and three space dimensions local in time existence and uniqueness of a solution is proved. We show that for discontinuous initial perturbations this solution is infinitely differentiable with respect to time t and space co-ordinates for t>0 on a bounded time interval. 相似文献