On Some Boundary Element Methods for the Heat Equation.
S. Kesavan, A.s. Vasudevamurthy (1985)
Numerische Mathematik
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S. Kesavan, A.s. Vasudevamurthy (1985)
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M. Shah (1973)
Matematički Vesnik
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Zayed, E.M.E. (1997)
International Journal of Mathematics and Mathematical Sciences
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W. Mydlarczyk (1987)
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Ján Filo, Stephan Luckhaus (2000)
Journal of the European Mathematical Society
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An asymptotic analysis is given for the heat equation with mixed boundary conditions rapidly oscillating between Dirichlet and Neumann type. We try to present a general framework where deterministic homogenization methods can be applied to calculate the second term in the asymptotic expansion with respect to the small parameter characterizing the oscillations.
E. M. E. Zayed (2000)
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Mathematische Zeitschrift
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М.Г. Опаец, В.П. Деркач, В.Г. Сучеван (1982)
Matematiceskie issledovanija
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Buschman, R.G. (1983)
International Journal of Mathematics and Mathematical Sciences
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W Golik (1991)
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Jifeng Chu, Daqing Jiang, Donal O'Regan, R. P. Agarwal (2005)
Applicationes Mathematicae
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We study the existence of positive solutions to second order nonlinear differential equations with Neumann boundary conditions. The proof relies on a fixed point theorem in cones, and the positivity of Green's function plays a crucial role in our study.