In this paper, we consider initial-boundary value problem on a semiaxis for the generalized Kawahara equation with higher-order nonlinearity. We obtain result existence and uniqueness of global solution. Also, if contains an absorbing term vanishing at infinity, prove that solution decays large time values.

We investigate an initial-boundary value problem for a time-fractional subdiffusion equation with the Caputo derivatives on $N$-dimensional torus by classical Fourier method. Since our solution is established eigenfunction expansion of elliptic operator, method proposed in this article can be used to arbitrary domain and operator variable coefficients. It should noted that conditions existence ...