Parameter identification for an abstract Cauchy problem by quasilinearization
Abstract : A parameter identification problem is considered in the context of a linear abstract Cauchy problem with a parameter-dependent evolution operator. Conditions are investigated under which the gradient of the state with respect to a parameter possesses smoothness properties which lead to local convergence of an estimation algorithm based on quasilinearization. Numerical results are presented concerning estimation of unknown parameters in delay-differential equations. (JHD)
PRIMERAS JORNADAS SOBRE ECUACIONES DIFERENCIALES, OPTIMIZACIÓN Y ANÁLISIS NUMÉRICO
In this paper we do the mathematical analysis of the problem which was analysed in S.M. Zubair M.A. Chaudhry, Warmeund Stoffubertragung, 30 (1994), 77-81. We consider the solidification of a semi-infinite material which is initially at its liquid phase at a uniform temperature Ti. Suddenly at time t > 0 the fixed face x = 0 is submitted to a convective cooling condition with a time-dependent heat transfer coefficient of the type h (t) = h0t −1/2 (h0 > 0) . The bulk temperature of the liquid at a large distance from the solid-liquid interface is T∞, a constant temperature such that T∞ kl √ παl Ti−Tf Ti−T∞ where kl and αl are the conductivity and diffusion coefficients of the initial liquid phase.
NUMERICAL CAMPEDELLI SURFACES WITH FUNDAMENTAL GROUP OF ORDER 9
We give explicit constructions of all the numerical Cam\-pe\-delli surfaces, i.e.\ the minimal surfaces of general type with $K^2=2$ and $p_g=0$, whose fundamental group has order 9. There are three families, one with $\pionealg=\Z_9$ and two with $\pionealg=\Z_3^2$. We also determine the base locus of the bicanonical system of these surfaces. It turns out that for the surfaces with $\pionealg=\Z_9$ and for one of the families of surfaces with $\pionealg=\Z_3^2$ the base locus consists of two points. To our knowlegde, these are the only known examples of surfaces of general type with $K^2>1$ whose bicanonical system has base points.