Advanced Search

The existence, uniqueness and regularity of the generalized local solution and the classical local solution to the periodic boundary value problem and Cauchy problem for the multidimensional coupled system of a nonlinear complex Schrödinger equation and a generalized IMBq equation $$i{\epsilon }_t+{\nabla }^2\epsilon -u\epsilon =0,$$ $$u_{tt}-{\nabla }^{2}u-a{\nabla }^2{u}_{tt}={\nabla }^{2}f\left(u\right)+{\nabla }^2{\left(\right|\epsilon |}^2)$$ are proved.

We establish the asymptotic stability of solutions of the mixed problem for the nonlinear evolution equation $\left(\right|u_t{{|}^{r-2}{u}_t)}_t-\Delta u_{tt}-\Delta u-\delta \Delta u_t=f\left(u\right)$.