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  • 1
    Electronic Resource
    Electronic Resource
    Galerkin approximation for inverse problems for nonautonomous nonlinear distributed systems (1991)
    Springer
    Applied mathematics & optimization 24 (1991), S. 233-256 
    Details
    ISSN: 1432-0606
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We develop an abstract framework and convergence theory for Galerkin approximation for inverse problems involving the identification of nonautonomous, in general nonlinear, distributed parameter systems. We provide a set of relatively easily verified conditions which are sufficient to guarantee the existence of optimal solutions and their approximation by a sequence of solutions to a sequence of approximating finite-dimensional identification problems. Our approach is based upon the theory of monotone operators in Banach spaces and is applicable to a reasonably broad class of nonlinear distributed systems. Operator theoretic and variational techniques are used to establish a fundamental convergence result. An example involving evolution systems with dynamics described by nonstationary quasi-linear elliptic operators along with some applications and numerical results are presented and discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01447744
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Statistical methods for model comparison in parameter estimation problems for distributed systems (1990)
    Springer
    Journal of mathematical biology 28 (1990), S. 501-527 
    Details
    ISSN: 1432-1416
    Keywords: Hypothesis testing ; Parameter estimation ; Partial differential equations ; Approximation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In this note we outline some recent results on the development of a statistical testing methodology for inverse problems involving partial differential equation models. Applications to several problems from biology are presented. The statistical tests, which are in the spirit of analysis of variance (ANOVA), are based on asymptotic distributional results for estimators and residuals in a least squares approach.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00164161
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Estimation of growth and survival in size-structured cohort data: an application to larval striped bass (Morone saxatilis) (1991)
    Springer
    Journal of mathematical biology 30 (1991), S. 125-150 
    Details
    ISSN: 1432-1416
    Keywords: Size-structural population models ; Parameter estimation ; Growth and mortality rates
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We present a method for estimating growth and mortality rates in size-structured population models. The methods are based on least-square fits to data using approximate models (using spline approximations) for the underlying partial differential equation population model. In a series of numerical tests, we compare our approach to an existing method (due to Hackney and Webb). As an example, we apply our techniques to experimental data from larval striped bass field studies.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00160331
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    Paper (German National Licenses)
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