ALBERT

All Library Books, journals and Electronic Records Telegrafenberg

X
feed icon rss

Your email was sent successfully. Check your inbox.

An error occurred while sending the email. Please try again.

Proceed reservation?

Export
  • 1
    Electronic Resource
    Electronic Resource
    On the integral equation method for the plane mixed boundary value problem of the Laplacian (1979)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 1 (1979), S. 265-321 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Although the plane boundary value problem for the Laplacian with given Dirichlet data on one part Γ2 and given Neumann data on the remaining part Γ2 of the boundary is the simplest case of mixed boundary value problems, we present several applications in classical mathematical physics. Using Green's formula the problem is converted into a system of Fredholm integral equations for the yet unknown values of the solution u on Γ2 and the also desired values of the normal derivatie on Γ1. One of these equations has principal part of the second kind, whereas that one of the other is of the first kind. Since any improvement of constructive methods requires higher regularity of u but, on the other hand, grad u possesses singularities at the collision points Γ1 ∩ Γ2 even for C∞ data, u is decomposed into special singular terms and a regular rest. This is incorporated into the integral equations and the modified system is solved in appropriate Sobolev spaces. The solution of the system requires to solve a Fredholm equation of the first kind on the arc Γ2 providing an improvement of regularity for the smooth part of u. Since the integral equations form a strongly elliptic system of pseudodifferential operators, the Galerkin procedure converges. Using regular finite element functions on Γ1 and Γ2 augmented by the special singular functions we obtain optimal order of asymptotic convergence in the norm corresponding to the energy norm of u and also superconvergence as well as high orders in smoother norms if the given data are smooth (and not the solution).
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670010302
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 2
    Electronic Resource
    Electronic Resource
    Plane potential flow past a cylinder with porous surface (1987)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 9 (1987), S. 587-605 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In the paper two models for the potential flow past a cylinder with porous or perforated surface are reduced to nonlinear Riemann-Hilbert problems for the complex velocity function and general existence and uniqueness theorems for the solution of the problems are derived. Further the problems are reduced to nonlinear singular integral equations of Hilbert type whose solvability is investigated by means of the Schauder and Banach fixed point theorem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670090137
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 3
    Electronic Resource
    Electronic Resource
    Boundary control of a vibrating plate with internal damping (1989)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 11 (1989), S. 573-586 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: It is shown that finite energy states of a vibrating viscoelastic plate of the Kelvin-Voigt type are, in general, not exactly controllable by L2-boundary controls. Accordingly, we present a result on approximative controllability. The method is general.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670110502
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 4
    Electronic Resource
    Electronic Resource
    Conform and mixed finite element schemes for the Dirichlet problem for the Bilaplacian in plane domains with corners (1979)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 1 (1979), S. 354-382 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In plane domains with corners for the Bilaplacian a uniquely solvable conform variational principle is studied on weighted Sobolev spaces which is equivalent to the standard Dirichlet problem in the weak form. Clamped plates under point forces near corners are handled by this approach. With weighted Hsieh-Clough-Tocher elements on regular triangulations as conform C1-finite elements a new error analysis is performed without higher regularity assumptions on the exact solution than given by the data and the boundary. The rate of convergence of the error depends on the eigenvalue with smallest imaginary part of a clamped infinite wedge since this eigenvalue describes the singularity of the exact solution in a sector with same angle. Using different spaces of trial and test functions in the standard Galerkin procedure it is shown that the error in the weighted energy norm does not pollute. For convex corners asymptotic error estimates, are proved yielding convergence for a mixed method in hydrodynamics where the solution of a system of 2nd order and its Laplacian are approximated simultaneously by C0-finite elements being piecewise polynomials.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670010305
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 5
    Electronic Resource
    Electronic Resource
    The sommerfeld half-plane problem revisited I: The solution of a pair of coupled Wiener-Hopf integral equationsPresented at a Conference in Diffraction and Scattering Theory held at the Technische Hochschule Darmstadt on May 29, 1980. (1982)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 4 (1982), S. 74-90 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A study and the solution of an extension of the classical Sommerfeld half-plane problem which leads to a pair of integral equations of the Wiener-Hopf type is given. The method of solution is function theoretic in character and employs a combination of the ideas of Wiener and Hopf and Carleman.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670040106
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 6
    Electronic Resource
    Electronic Resource
    The sommerfeld half-plane problem revisited III: Parallel plate media with mixed boundary conditionsThe results of this paper were announced at the XXth General Assembly of the U.R.S.I. held in Washington, D.C. in August 1981. (1983)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 5 (1983), S. 257-275 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A plane wave is normally incident upon an infinite stack of equally spaced parallel plates which are semi-infinite and not staggered. The plates satisfy the so-called “Rawlins” boundary conditions. This problem is formulated as a pair of simultaneous integral equations of the Wiener-Hopf type and solved by a method proposed by A. E. Heins in 1950.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670050118
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 7
    Electronic Resource
    Electronic Resource
    A fast solver for riemann problems (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 101-107 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: An efficient algorithm is presented for solving the Riemann problem for a polytropic gas. It enables the user to compute the solution for all physically reasonable data. The convergence of the algorithm is proved. The accuracy of the solution is limited only by the accuracy of the computer. There is an a-priori estimation of the required number of iterations. The rate of convergence turns out to be much higher than that of the usual fixed point iteration scheme.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670070107
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 8
    Electronic Resource
    Electronic Resource
    Modelling of dynamic networks of thin thermoelastic beams (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 327-358 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We derive a distributed-parameter model of a thin non-linear thermoelastic beam in three dimensions. The beam can also be initially curved and twisted. Our main task is to formulate the non-homogeneous initial, boundary and node value problem associated with the dynamics of a network of a finite number of such beams. The emphasis here is on a distributed-parameter modelling of the geometric and kinematic node conditions. The forces and couples appearing in the boundary and node conditions can then be viewed as control variables. The analysis of the resulting control systems and their controllability and stabilizability properties is the subject of [25] and of forthcoming papers.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670160503
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 9
    Electronic Resource
    Electronic Resource
    The sommerfeld half-plane problem revisited, II the factoring of a matrix of analytic functionsThese results were announced at the XXth General Assembly of the U.R.S.I. held in Washington, D.C., August 1981. (1983)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 5 (1983), S. 14-21 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A half-plane under plane wave excitation obeys a Dirichlet boundary condition on one side and a Neumann boundary condition on the other. These boundary conditions contrast the ones used by A. Sommerfeld in his classical paper. The present problem leads to a system of integral equations of the Wiener-Hopf type which may be solved by a matrix factoring method suggested by A. E. Heins in 1950.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670050103
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 10
    Electronic Resource
    Electronic Resource
    Optimal control problems in diffusion processes with a nonsmooth nonlinear boundary condition (1983)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 5 (1983), S. 117-130 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We investigate a one-dimensional diffusion process controlled by a nonsmooth nonlinear boundary condition. Existence and estimates of positive solutions of the differential equation are derived. We prove necessary conditions for optimal controls and apply them to two examples.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670050109
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
Close ⊗
This website uses cookies and the analysis tool Matomo. More information can be found here...