Upper semicontinuity of the attractor for a singularly perturbed hyperbolic equation
نویسندگان
چکیده
منابع مشابه
Approximation of singularly perturbed linear hyperbolic systems
This paper is concerned with systems modelled by linear singularly perturbed partial differential equations. More precisely a class of linear systems of conservation laws with a small perturbation parameter is investigated. By setting the perturbation parameter to zero, the full system leads to two subsystems, the reduced system standing for the slow dynamics and the boundary-layer system repre...
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The work [1] is generalized to the singularly perturbed nonlinear Schrödinger (NLS) equation of which the regularly perturbed NLS studied in [1] is a mollification. Specifically, the existence of Smale horseshoes and Bernoulli shift dynamics is established in a neighborhood of a symmetric pair of Silnikov homoclinic orbits under certain generic conditions, and the existence of the symmetric pai...
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has a solution «=g(x) for O^x^Xo with g(0)=a and u = h(x) tor xo^x^l with h(l)=b where g(x0)=h(x0). It will be assumed that g'(xo)*h'(xo). The case of (1) with f=l — (y')t and where \a — b\ <1 can be treated explicitly. For small e>0 the solution of (1) tends to the broken line solution of (2) with g(x)=a — x and h = b — 1+x and Xo = (l+a—b)/2. (There is another broken line solution of (2) with...
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In this paper an exponentially fitted finite difference method is presented for solving singularly perturbed two-point boundary value problems with the boundary layer. A fitting factor is introduced and the model equation is discretized by a finite difference scheme on an uniform mesh. Thomas algorithm is used to solve the tri-diagonal system. The stability of the algorithm is investigated. It ...
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Our aim in this article is to construct exponential attractors for singularly perturbed damped wave equations that are continuous with respect to the perturbation parameter. The main difficulty comes from the fact that the phase spaces for the perturbed and unperturbed equations are not the same; indeed, the limit equation is a (parabolic) reaction-diffusion equation. Therefore, previous constr...
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ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 1988
ISSN: 0022-0396
DOI: 10.1016/0022-0396(88)90104-0