Seminar 鈥淜inetic and nonlinear equations of mathematical physics鈥�
9 March at 18:00 (Moscow time)
Speaker: Solonukha O.V.
Topic: Existence of solutions of linear and nonlinear differential equations of parabolic type with nonlocal boundary conditions of the Bitsadze-Samarsky type.
Differential equations of parabolic type in a bounded cylinder are considered. Boundary conditions of the Bitsadze-Samarsky type connect the values of the function at the cylinder boundary with the values inside the cylinder. Under certain conditions, the boundary conditions of the Bitsadze-Samarsky type correspond to 邪 difference operator, which is an isomorphism between the Sobolev space with homogeneous boundary conditions and the Sobolev space with nonlocal boundary conditions of the Bitsadze-Samarsky type. The solvability of the original parabolic differential equation is justified by the solvability of the corresponding parabolic differential-difference equation.