On the Existence of Time-Periodic Solutions of Nonlinear Parabolic Differential Equations with Nonlocal Boundary Conditions of the Bitsadze–Samarskii Type
摘要
We study a nonlinear parabolic differential equation in a bounded multidimensional domain with nonlocal boundary conditions of the Bitsadze–Samarskii type. We prove existence theorems for a periodic in time generalized solution. Sufficient conditions for the existence of generalized solutions contain either an algebraic ellipticity condition or an algebraic strong ellipticity condition for an auxiliary differential-difference operator.