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  • NUMERICAL ANALYSIS  (4)
  • Existence and uniqueness  (1)
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  • 1
    Electronic Resource
    Electronic Resource
    On the stationary semiconductor equations arising in modeling an LBIC technique (1996)
    Springer
    Applied mathematics & optimization 33 (1996), S. 189-202 
    Details
    ISSN: 1432-0606
    Keywords: Existence and uniqueness ; Semiconductor equations ; LBIC ; 35J65 ; 35D05
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper by using anL ∞ estimate for elliptic equations, we study the well-posedness of the stationary semiconductor equations arising from modeling a nondestructive testing technique LBIC. It is shown that when the extra source term is small, the system has a unique weak solution, and the solution is continuously dependent on this source term. The validity of an approximate model derived for the study of the inverse problem is established. The existence result is then extended to the case of constant mobilities without the assumption on the size of the source term.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01183143
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    Paper (German National Licenses)
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  • 2
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    On non-convergence of adjoint semigroups for control systems with delays (1987)
    In:  CASI
    Details
    Publication Date: 2019-06-28
    Description: It is shown that the adjoints of a spline based approximation scheme for delay equations do not converge strongly.
    Keywords: NUMERICAL ANALYSIS
    Type: NASA-CR-178342 , ICASE-87-47 , NAS 1.26:178342 , AD-A192761
    Format: application/pdf
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    NASA TECHNICAL REPORTS
  • 3
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    The augmented Lagrangian method for parameter estimation in elliptic systems (1990)
    In:  Other Sources
    Details
    Publication Date: 2019-07-12
    Description: In this paper a new technique for the estimation of parameters in elliptic partial differential equations is developed. It is a hybrid method combining the output-least-squares and the equation error method. The new method is realized by an augmented Lagrangian formulation, and convergence as well as rate of convergence proofs are provided. Technically the critical step is the verification of a coercivity estimate of an appropriately defined Lagrangian functional. To obtain this coercivity estimate a seminorm regularization technique is used.
    Keywords: NUMERICAL ANALYSIS
    Type: SIAM Journal on Control and Optimization (ISSN 0363-0129); 28; 113-136
    Format: text
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    NASA TECHNICAL REPORTS
  • 4
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    Legendre-tau approximation for functional differential equations. II - The linear quadratic optimal control problem (1987)
    In:  Other Sources
    Details
    Publication Date: 2019-07-12
    Description: The numerical scheme based on the Legendre-tau approximation is proposed to approximate the feedback solution to the linear quadratic optimal control problem for hereditary differential systems. The convergence property is established using Trotter ideas. The method yields very good approximations at low orders and provides an approximation technique for computing closed-loop eigenvalues of the feedback system. A comparison with existing methods (based on averaging and spline approximations) is made.
    Keywords: NUMERICAL ANALYSIS
    Type: SIAM Journal on Control and Optimization (ISSN 0363-0129); 25; 1379-140
    Format: text
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    NASA TECHNICAL REPORTS
  • 5
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    Finite-dimensional compensators for infinite-dimensional systems via Galerkin-type approximation (1990)
    In:  Other Sources
    Details
    Publication Date: 2019-07-12
    Description: In this paper existence and construction of stabilizing compensators for linear time-invariant systems defined on Hilbert spaces are discussed. An existence result is established using Galkerin-type approximations in which independent basis elements are used instead of the complete set of eigenvectors. A design procedure based on approximate solutions of the optimal regulator and optimal observer via Galerkin-type approximation is given and the Schumacher approach is used to reduce the dimension of compensators. A detailed discussion for parabolic and hereditary differential systems is included.
    Keywords: NUMERICAL ANALYSIS
    Type: SIAM Journal on Control and Optimization (ISSN 0036-1410); 28; 1251-126
    Format: text
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    NASA TECHNICAL REPORTS
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