We found a match
Your institution may have rights to this item. Sign in to continue.
- Title
Periodic problem for an evolution equation with a quadratic and a cubic nonlinearity.
- Authors
Komarov, M.
- Abstract
We study conditions for the existence of a solution of a periodic problem for a model nonlinear equation in the spatially multidimensional case and consider various types of large time asymptotics (exponential and oscillating) for such solutions. The generalized Kolmogorov-Petrovskii-Piskunov equation, the nonlinear Schrödinger equation, and some other partial differential equations are special cases of this equation. We analyze the solution smoothing phenomenon under certain conditions on the linear part of the equation and study the case of nonsmall initial data for a nonlinearity of special form. The leading asymptotic term is presented, and the remainder in the asymptotics of the solution is estimated in a spatially uniform metric.
- Subjects
NONLINEAR theories; EVOLUTION equations; ASYMPTOTIC theory in nonlinear differential equations; PARTIAL differential equations; BESSEL functions
- Publication
Differential Equations, 2011, Vol 47, Issue 12, p1726
- ISSN
0012-2661
- Publication type
Article
- DOI
10.1134/S0012266111120032