A singular Gierer—Meinhardt system of elliptic equations
Y. S. Choi, P. J. McKenna (2000)
Annales de l'I.H.P. Analyse non linéaire
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Y. S. Choi, P. J. McKenna (2000)
Annales de l'I.H.P. Analyse non linéaire
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Louro, Bento (1991)
Portugaliae mathematica
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Mark Williams (2000)
Annales scientifiques de l'École Normale Supérieure
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Howard G. Bergmann (1953)
Compositio Mathematica
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Ivan Hlaváček (1990)
Aplikace matematiky
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A second order elliptic problem with axisymmetric data is solved in a finite element space, constructed on a triangulation with curved triangles, in such a way, that the (nonhomogeneous) boundary condition is fulfilled in the sense of a penalty. On the basis of two approximate solutions, extrapolates for both the solution and the boundary flux are defined. Some a priori error estimates are derived, provided the exact solution is regular enough. The paper extends some of the results of...
S. N. Antontsev, A. M. Meirmanov, V. V. Yurinsky (2004)
Bollettino dell'Unione Matematica Italiana
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We analyze existence and uniqueness of weak solutions to the well-posed Hele-Shaw problem under general conditions on the fixed boundaries and non-homogeneous governing equation in the unknown domain and non-homogeneous dynamic condition on the free boundary. Our approach allows us also to minimize the restrictions on the boundary and initial data. We derive several estimates on the solutions in spaces, prove a comparison theorem, and show that the solution depends continuously on...