We give an interpretation of the hemisphere rigidity theorem Hang-Wang in framework Gelfand problem. More precisely, showed that for a metric $ g conformal to standard g_0 on S^{n}_{+} with R\geq n(n-1) and whose boundary coincides g_0|_{\partial S^{n}_{+}} $, then = $. This is related classical problem, which investigates -\Delta u \lambda g(u) certain nonlinearity bounded region \Omega \subse...

We consider a generalization of the Gelfand problem arising in Frank-Kamenetskii theory of thermal explosion. This generalization is a natural extension of the Gelfand problem to two-phase materials, where, in contrast to the classical Gelfand problem which uses a single temperature approach, the state of the system is described by two different temperatures. We show that similar to the classic...

in this work, we study the performance of the sinc-collocation method for solving bratu's problem. for different choices of step size, we consider the maximum absolute errors in the solutions at sinc grid points and tabulated in tables. the comparison of the obtained results veri ed that this method converges to the exact solution rapidly and with

We present a constructive proof of Gelfand duality for C*-algebras by reducing the problem to Gelfand duality for real C*-algebras.