Abstract
This work concerns the factorization of a second order elliptic boundary value problem defined in a star-shaped bounded regular domain, in a system of uncoupled first order initial value problems, using the technique of invariant embedding. The family of domains is defined by a homothety. The method yields an equivalent formulation to the initial boundary value problem by a system of two uncoupled Cauchy problems. The singularity at the origin of the homothety is studied.
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References
Bellman, R.: Dynamic Programming. Princeton University Press, Princeton (1957)
Gilbarg, D., Trudinger, N.: Elliptic Partial Differential Equations of Second Order. Springer, Berlin (1983)
Henry, J., Louro, B., Soares, M.C.: A factorization method for elliptic problems in a circular domain. C. R. Math. Acad. Sci. 339(3), 175–180 (2004)
Henry, J., Ramos, A.: Factorization of second order elliptic boundary value problems by dynamic programming. Nonlinear Analysis 59, 629–647 (2004)
Henry, J., Ramos, A.: Study of the initial value problems appearing in a method of factorization of second-order elliptic boundary value problems. Nonlinear Analysis 68, 2984–3008 (2008)
Lions, J.L.: Optimal Control of Systems Governed by Partial Differential Equations. Springer, New York (1971)
Soares, M.C.: Factorization by Invariant Embedding of Elliptic Problems: Circular and Star-shaped Domains, PhD Thesis, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa (2006)
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Henry, J., Louro, B., Soares, M.C. (2009). Factorization by Invariant Embedding of a Boundary Value Problem for the Laplace Operator. In: Korytowski, A., Malanowski, K., Mitkowski, W., Szymkat, M. (eds) System Modeling and Optimization. CSMO 2007. IFIP Advances in Information and Communication Technology, vol 312. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04802-9_15
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DOI: https://doi.org/10.1007/978-3-642-04802-9_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-04801-2
Online ISBN: 978-3-642-04802-9
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