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  • Articles  (10)
  • Other Sources
  • Articles: DFG German National Licenses  (10)
  • Optimal control  (4)
  • AMS(MOS): 65N30  (3)
  • Bifurcation  (3)
  • 1980-1984  (10)
  • Mathematics  (10)
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  • Articles  (10)
  • Other Sources
Source
  • Articles: DFG German National Licenses  (10)
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Year
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  • 1
    Electronic Resource
    Electronic Resource
    On conforming finite element methods for the inhomogeneous stationary Navier-Stokes equations (1983)
    Springer
    Numerische Mathematik 42 (1983), S. 173-194 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We consider the stationary Navier-Stokes equations, written in terms of the primitive variables, in the case where both the partial differential equations and boundary conditions are inhomogeneous. Under certain conditions on the data, the existence and uniqueness of the solution of a weak formulation of the equations can be guaranteed. A conforming finite element method is presented and optimal estimates for the error of the approximate solution are proved. In addition, the convergence properties of iterative methods for the solution of the discrete nonlinear algebraic systems resulting from the finite element algorithm are given. Numerical examples, using an efficient choice of finite element spaces, are also provided.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01395310
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  • 2
    Electronic Resource
    Electronic Resource
    Approximation of tricomi problem with Neumann boundary condition (1984)
    Springer
    Numerische Mathematik 44 (1984), S. 371-391 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: G 1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The Tricomi problem with Neumann boundary condition is reduced to a degenerate problem in the elliptic region with a non-local boundary condition and to a Cauchy problem in the hyperbolic region. A variational formulation is given to the elliptic problem and a finite element approximation is studied. Also some regularity results in weighted Sobolev spaces are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01405569
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  • 3
    Electronic Resource
    Electronic Resource
    On mixed finite element methods for first order elliptic systems (1981)
    Springer
    Numerische Mathematik 37 (1981), S. 29-48 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A physically based duality theory for first order elliptic systems is shown to be of central importance in connection with the Galerkin finite element solution of these systems. Using this theory in conjunction with a certain hypothesis concerning approximation spaces, optimal error estimates for Galerkin type approximations are demonstrated. An example of a grid which satisfies the hypothesis is given and numerical examples which illustrate the theory are provided.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396185
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  • 4
    Electronic Resource
    Electronic Resource
    Bifurcations at a cusp singularity with applications (1984)
    Springer
    Acta applicandae mathematicae 2 (1984), S. 101-138 
    Details
    ISSN: 1572-9036
    Keywords: 58F ; 70K ; 92 ; Bifurcation ; vector field ; saddle-node singularity ; cusp singularity ; saddle connection ; normal form ; unfolding ; versal family ; population dynamics ; oscillators
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider families of vector fields which exhibit a cusp singularity for some values of the parameters. Algebraic conditions are obtained for these families to have versal properties. This enables the topologically distinct, structurally stable types of phase portrait which occur in the family near to the bifurcation point to be predicted. Applications of these results in population dynamics and oscillation theory are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00046575
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  • 5
    Electronic Resource
    Electronic Resource
    Hopf bifurcation in a stomatal oscillator (1982)
    Springer
    Journal of mathematical biology 12 (1982), S. 1-11 
    Details
    ISSN: 1432-1416
    Keywords: Bifurcation ; Stomata ; Oscillation ; Nonlinear dynamics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Stomata are microscopic openings in leaves of green plants which permit gas exchange. This paper presents a parameter study of a model of a stomatal oscillator first derived by Delwiche and Cooke in 1977. We prove the existence of an unstable limit cycle by using the theory of the Hopf bifurcation. Other bifurcations exhibited by the model are also discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00275199
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  • 6
    Electronic Resource
    Electronic Resource
    A model of evolutionary appearance of dissipative structure in ecosystems (1983)
    Springer
    Journal of mathematical biology 18 (1983), S. 13-23 
    Details
    ISSN: 1432-1416
    Keywords: Ecosystem ; Evolution ; Autonomous oscillations ; issipative structure ; Bifurcation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The interrelation between autonomous oscillations in local systems and stable dissipative structures in spatially distributed systems is analyzed. Darwinian evolution in populations comprising the ecosystem is shown to be able to cause the qualitative rearrangements of dynamic modes and smooth appearance of oscillations in local systems. The same evolutionary mechanisms analyzed within bilocal systems, may lead to appearance of dissipative structures (both smooth and sharp).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00275907
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  • 7
    Electronic Resource
    Electronic Resource
    An exact penalty function algorithm for optimal control problems with control and terminal equality constraints, part 1 (1980)
    Springer
    Journal of optimization theory and applications 32 (1980), S. 211-246 
    Details
    ISSN: 1573-2878
    Keywords: Optimal control ; control constraints ; terminal equality constraints ; exact penalty function ; convergence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The presence of control constraints, because they are nondifferentiable in the space of control functions, makes it difficult to cope with terminal equality constraints in optimal control problems. Gradient-projection algorithms, for example, cannot be employed easily. These difficulties are overcome in this paper by employing an exact penalty function to handle the cost and terminal equality constraints and using the control constraints to define the space of permissible search directions in the search-direction subalgorithm. The search-direction subalgorithm is, therefore, more complex than the usual linear program employed in feasible-directions algorithms. The subalgorithm approximately solves a convex optimal control problem to determine the search direction; in the implementable version of the algorithm, the accuracy of the approximation is automatically increased to ensure convergence.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00934725
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  • 8
    Electronic Resource
    Electronic Resource
    An exact penalty function algorithm for optimal control problems with control and terminal equality constraints, part 2 (1980)
    Springer
    Journal of optimization theory and applications 32 (1980), S. 345-364 
    Details
    ISSN: 1573-2878
    Keywords: Optimal control ; control constraints ; terminal equality constraints ; exact penalty functions ; convergence ; relaxed control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In Part 1 of this paper, implementable and conceptual versions of an algorithm for optimal control problems with control constraints and terminal equality constraints were presented. It was shown that anyL ∞ accumulation points of control sequences generated by the algorithms satisfy necessary conditions of optimality. Since such accumulation points need not exist, it is shown in this paper that control sequences generated by the algorithms always have accumulation points in the sense of control measure, and these accumulation points satisfy optimality conditions for the corresponding relaxed control problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00934557
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  • 9
    Electronic Resource
    Electronic Resource
    Convergence of a strong variational algorithm for relaxed controls involving a class of hyperbolic systems (1984)
    Springer
    Journal of optimization theory and applications 42 (1984), S. 467-485 
    Details
    ISSN: 1573-2878
    Keywords: Optimal control ; hyperbolic partial differential equations ; Darboux boundary conditions ; strong variational algorithm ; convergence ; relaxed control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we consider a class of optimal control problems involving linear hyperbolic partial differential equations with Darboux boundary conditions. A strong variational algorithm has been obtained for solving this class of optimal control problems in a previous paper by the third and the first authors. It was also shown that anyL ∞ accumulation points of control sequences generated by the algorithm satisfy a necessary condition for optimality. Since such accumulation points need not exist, it is shown in this paper that the control sequences generated by the algorithm always have accumulation points in the sense of control measure, and these accumulation points satisfy a necessary condition for optimality for the corresponding relaxed control problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00935327
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  • 10
    Electronic Resource
    Electronic Resource
    Second-order necessary conditions in optimal control: Accessory-problem results without normality conditions (1983)
    Springer
    Journal of optimization theory and applications 41 (1983), S. 75-106 
    Details
    ISSN: 1573-2878
    Keywords: Optimal control ; second-order necessary conditions ; accessory problem ; control constraints ; normality condition
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract An optimal control problem, which includes restrictions on the controls and equality/inequality constraints on the terminal states, is formulated. Second-order necessary conditions of the accessory-problem type are obtained in the absence of normality conditions. It is shown that the necessary conditions generalize and simplify prior results due to Hestenes (Ref. 5) and Warga (Refs. 6 and 7).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00934437
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