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Cauchy Data (cauchy + data)
Selected AbstractsDetermining the temperature from incomplete boundary dataMATHEMATISCHE NACHRICHTEN, Issue 16 2007B. Tomas Johansson Abstract An iterative procedure for determining temperature fields from Cauchy data given on a part of the boundary is presented. At each iteration step, a series of mixed well-posed boundary value problems are solved for the heat operator and its adjoint. A convergence proof of this method in a weighted L2 -space is included, as well as a stopping criteria for the case of noisy data. Moreover, a solvability result in a weighted Sobolev space for a parabolic initial boundary value problem of second order with mixed boundary conditions is presented. Regularity of the solution is proved. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] An iterative procedure for solving a Cauchy problem for second order elliptic equationsMATHEMATISCHE NACHRICHTEN, Issue 1 2004Tomas JohanssonArticle first published online: 14 JUL 200 Abstract An iterative method for reconstruction of solutions to second order elliptic equations by Cauchy data given on a part of the boundary, is presented. At each iteration step, a series of mixed well-posed boundary value problems are solved for the elliptic operator and its adjoint. The convergence proof of this method in a weighted L2 space is included. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Almost global existence for Hamiltonian semilinear Klein-Gordon equations with small Cauchy data on Zoll manifoldsCOMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 11 2007D. Bambusi This paper is devoted to the proof of almost global existence results for Klein-Gordon equations on Zoll manifolds (e.g., spheres of arbitrary dimension) with Hamiltonian nonlinearities, when the Cauchy data are smooth and small. The proof relies on Birkhoff normal form methods and on the specific distribution of eigenvalues of the Laplacian perturbed by a potential on Zoll manifolds. © 2007 Wiley Periodicals, Inc. [source] |