The Davey–Stewartson I equation on the quarter plane with homogeneous Dirichlet boundary conditions
نویسندگان
چکیده
منابع مشابه
The Davey-Stewartson I Equation on the Quarter Plane with Homogeneous Dirichlet Boundary Conditions
Dromions are exponentially localised coherent structures supported by nonlinear integrable evolution equations in two spatial dimensions. In the study of initial-value problems on the plane, such solutions occur only if one imposes nontrivial boundary conditions at infinity, a situation of dubious physical significance. However it is established here that dromions appear naturally in the study ...
متن کاملA Non-homogeneous Boundary-value Problem for the Korteweg-de Vries Equation in a Quarter Plane
The Korteweg-de Vries equation was first derived by Boussinesq and Korteweg and de Vries as a model for long-crested small-amplitude long waves propagating on the surface of water. The same partial differential equation has since arisen as a model for unidirectional propagation of waves in a variety of physical systems. In mathematical studies, consideration has been given principally to pure i...
متن کاملRefined asymptotics for the infinite heat equation with homogeneous Dirichlet boundary conditions
The nonnegative viscosity solutions to the infinite heat equation with homogeneous Dirichlet boundary conditions are shown to converge as t → ∞ to a uniquely determined limit after a suitable time rescaling. The proof relies on the half-relaxed limits technique as well as interior positivity estimates and boundary estimates. The expansion of the support is also studied.
متن کاملDecay estimates for a viscous Hamilton-Jacobi equation with homogeneous Dirichlet boundary conditions
Global classical solutions to the viscous Hamilton-Jacobi equation ut −∆u = a |∇u| p in (0,∞) × Ω with homogeneous Dirichlet boundary conditions are shown to converge to zero in W (Ω) at the same speed as the linear heat semigroup when p > 1. For p = 1, an exponential decay to zero is also obtained in one space dimension but the rate depends on a and differs from that of the linear heat equatio...
متن کاملThe initial boundary problem for the Korteweg – de Vries equation on the negative quarter - plane
The initial boundary-value problem for the Korteweg–de Vries (KdV) equation on the negative quarter-plane, x < 0 and t > 0, is considered. The formulation of this problem is different to the usual initial boundary-value problem on the positive quarter-plane, for which x > 0 and t > 0. Two boundary conditions are required at x = 0 for the negative quarter-plane problem, in contrast to the one bo...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Physics
سال: 2003
ISSN: 0022-2488,1089-7658
DOI: 10.1063/1.1588744