منابع مشابه
On the Cauchy Problem and the Black Solitons of a Singularly Perturbed Gross-Pitaevskii Equation
We consider the one-dimensional Gross-Pitaevskii equation perturbed by a Dirac potential. Using a fine analysis of the properties of the linear propagator, we study the well-posedness of the Cauchy Problem in the energy space of functions with modulus 1 at infinity. Then we show the persistence of the stationary black soliton of the unperturbed problem as a solution. We also prove the existence...
متن کاملSingularly Perturbed Cauchy Problem for Abstract Linear Differential Equations of Second Order in Hilbert Spaces∗
We study the behavior of solutions to the problem { ε (u′′ ε (t) +A1uε(t)) + u ′ ε(t) +A0uε(t) = fε(t), t ∈ (0, T ), uε(0) = u0ε, uε(0) = u1ε, as ε → 0, where A1 and A0 are two linear self-adjoint operators in a Hilbert space H. MSC: 35B25, 35K15, 35L15, 34G10 keywords: singular perturbations; Cauchy problem; boundary layer function.
متن کاملQuasilinear singularly perturbed problem with boundary perturbation.
A class of quasilinear singularly perturbed problems with boundary perturbation is considered. Under suitable conditions, using theory of differential inequalities we studied the asymptotic behavior of the solution for the boundary value problem.
متن کاملNvestigation of a Boundary Layer Problem for Perturbed Cauchy-Riemann Equation with Non-local Boundary Condition
Boundary layer problems (Singular perturbation problems) more have been applied for ordinary differential equations. While this theory for partial differential equations have many applications in several fields of physics and engineering. Because of complexity of limit and boundary behavior of the solutions of partial differential equations these problems considered less than ordinary case. In ...
متن کاملA Uniformly Accurate Collocation Method for a Singularly Perturbed Problem
A semilinear singularly perturbed reaction-diffusion problem is considered and the approximate solution is given in the form of a quadratic polynomial spline. Using the collocation method on a simple piecewise equidistant mesh, an approximation almost second order uniformly accurate in small parameter is obtained. Numerical results are presented in support of this result. AMS Mathematics Subjec...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1979
ISSN: 0022-247X
DOI: 10.1016/0022-247x(79)90227-0