SOME QUESTIONS IN THE THEORY OF NONLINEAR ELLIPTIC AND PARABOLIC EQUATIONS
M I Višik, Andrei Vladimirovich Fursikov · Mathematics of the USSR-Sbornik · 1974
For the nonlinear parabolic equation of order (1)where the nonlinear part depends analytically on its arguments, in the case of periodic boundary conditions we prove a theorem about the unique solvability in a certain space of generalized functions if the initial condition is a generalized function from the same class. We prove an analogous theorem for nonlinear elliptic equations.We construct an asymptotic expansion (as ) for the th Fourier coefficient of the solution of a parabolic equation of the form (1).Bibliography: 3 items.