The paper deals with the existence of periodic solutions of the boundary value problem for nonlinear heat equation, where various types of nonlinearities are considered. The proofs are based on the investigation of Liapunov-Schmidt bifurcation system via Leray-Schauder degree theory.
We consider a model for transient conductive-radiative heat transfer in grey materials. Since the domain contains an enclosed cavity, nonlocal radiation boundary conditions for the conductive heat-flux are taken into account. We generalize known existence and uniqueness results to the practically relevant case of lower integrable heat-sources, and of nonsmooth interfaces. We obtain energy estimates that involve only the norm of the heat sources for exponents close to one. Such estimates are...