Dynamics of nonlinear parabolic systems with time delays
The authors consider the problem \[ u_t= \Delta u+ {\delta e^u \over \int_\Omega e^udx}, \quad (x,t) \in \Omega \times [0,T), \] \[ u(x,0) = u_0(x), \quad u(x,t) = 0,\;(x,t) \in \partial \Omega \times [0,T). \] This problem arises as a model for various interesting processes in engineering. The authors prove results on the steady state case, which are essentially the same as for the well known Gelfand problem (the problem without the integral in the denominator). They also prove existence results for the time dependent case.
scientific article; zbMATH DE number 906452