Fredagen den 6 oktober kl. 13.15--14.15 talar dr. Stig Larsson, CTH, om The qualitative behavior of finite element solutions of semilinear parabolic problems near stationary points.
Abstract. We study the qualitative behavior of finite element solutions of a semilinear parabolic problem near an unstable hyperbolic equilibrium. We show that any continuous trajectory is approximated by an appropriate discrete trajectory, and vice versa, as long as they remain in a sufficiently small neighborhood of the equilibrium. Error bounds of optimal order hold uniformly over arbitrarily long time intervals. In particular, the local stable and unstable manifolds of the discrete problem converge to their continuous counterparts. Therefore, the discretized dynamical system has the same qualitative behavior near the equilibrium as the continuous system. This is joint work with J.-M. Sanz-Serna, University of Valladolid. Fredagen den 13 oktober kl. 13.15--14.15 talar Pasi Mikkonen, Jyväskylä, om Potential estimates for p-superharmonic functions.
Abstract. We discuss pointwise estimates for supersolutions
of p-Laplacian type equations in terms of the Wolff potential
of the corresponding measure. Two applications of this
result are also discussed. First, the necessity of the
Wiener test for regularity of a boundary point, and secondly,
the self-improving property of uniform thickness.
Lokal: MAI:s seminarierum
Lars Inge Hedberg