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A necessary and sufficient condition for the existence of an exponential attractor

100%

Pražák D.

Open Mathematics

2003

tom 1

nr 3

411-417

We give a necessary and sufficient condition for the existence of an exponential attractor. The condition is formulated in the context of metric spaces. It also captures the quantitative properties of the attractor, i.e., the dimension and the rate of attraction. As an application, we show that the evolution operator for the wave equation with nonlinear damping has an exponential attractor.

Existence and nonexistence results for reaction-diffusion equations in product of cones

100%

Hamidi A., Laptev G.

Open Mathematics

2003

tom 1

nr 1

61-78

Problems of existence and nonexistence of global nontrivial solutions to quasilinear evolution differential inequalities in a product of cones are investigated. The proofs of the nonexistence results are based on the test-function method developed, for the case of the whole space, by Mitidieri, Pohozaev, Tesei and Véron. The existence result is established using the method of supersolutions.

Ograniczanie wyników

2 Open Mathematics

1 Hamidi A.

1 Laptev G.

1 Pražák D.

2 2003

Wyniki wyszukiwania

A necessary and sufficient condition for the existence of an exponential attractor

Existence and nonexistence results for reaction-diffusion equations in product of cones