Approximate solutions of eigenvalue problems with reproducing nonlinearities

Rutkowski, P.

doi:10.1007/bf00944852

Cited by 7 publications

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“…For the case of a scalar parabolic equation in one space dimension with a cubic nonlinearity, this latter property has been discussed for space approximation using the Conley index (Khalsa [22]). Numerical computations using Galerkin approximations have been done for a similar example (Mora [28], Rutkowski [30]). …”

Section: Introductionmentioning

confidence: 99%

Upper Semicontinuity of Attractors for Approximations of Semigroups and Partial Differential Equations

Hale¹,

Lin²,

Raugel³

1988

Mathematics of Computation

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Abstract.Suppose a given evolutionary equation has a compact attractor and the evolutionary equation is approximated by a finite-dimensional system. Conditions are given to ensure the approximate system has a compact attractor which converges to the original one as the approximation is refined. Applications are given to parabolic and hyperbolic partial differential equations. Introduction.Suppose A" is a Banach space and T(t), t > 0, is a Crsemigroup on X with r > 0; that is, T(t), t > 0, is a semigroup with T(t) continuous in t, x together with the derivatives in x up through the order r.Following standard terminology (see, for instance, Hale [12]), a set B C X is said to attract a set C C X under the semigroup T(t) if, for any e > 0, there is a t0 = t0(B,C,e) such that T(t)C C M(B,e) for t > t0, where M(B,e) denotes the

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Section: Introductionmentioning

confidence: 99%