A barrier method for quasilinear ordinary differential equations of the curvature type
Toshiaki Kusahara, Hiroyuki Usami (2000)
Czechoslovak Mathematical Journal
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Toshiaki Kusahara, Hiroyuki Usami (2000)
Czechoslovak Mathematical Journal
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Dirk Siersma (1999)
Banach Center Publications
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This paper studies the smoothness and the curvature of conflict sets of the distance function in the plane. Conflict sets are also well known as 'bisectors'. We prove smoothness in the case of two convex sets and give a formula for the curvature. We generalize moreover to weighted distance functions, the so-called Johnson-Mehl model.
Kroopnick, Allan (2008)
Applied Mathematics E-Notes [electronic only]
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Meunargia, T. (2004)
Bulletin of TICMI
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Purnaras, I.K. (2007)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
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Bofill, F., Quintanilla, R. (2003)
International Journal of Mathematics and Mathematical Sciences
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Svatoslav Staněk (1995)
Annales Polonici Mathematici
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The differential equation of the form , a ∈ (0,∞), is considered and solutions u with u(0) = 0 and (u(t))² + (u’(t))² > 0 on (0,∞) are studied. Theorems about existence, uniqueness, boundedness and dependence of solutions on a parameter are given.