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Solitary wave and other solutions for nonlinear heat equations

100%

Nikitin A., Barannyk T.

Open Mathematics

2004

tom 2

nr 5

840-858

A number of explicit solutions for the heat equation with a polynomial non-linearity and for the Fisher equation is presented. An extended class of non-linear heat equations admitting solitary wave solutions is described. The generalization of the Fisher equation is proposed whose solutions propagate with arbitrary ad hoc fixed velocity.

Finite dimensional global attractor for a class of doubly nonlinear parabolic equations

100%

Miranville A.

Open Mathematics

2006

tom 4

nr 1

163-182

Our aim in this paper is to study the long time behavior of a class of doubly nonlinear parabolic equations. In particular, we prove the existence of the global attractor which has, in one and two space dimensions, finite fractal dimension.

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

84%

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

3 Open Mathematics

1 Barannyk T.

1 Hamidi A.

1 Laptev G.

1 Miranville A.

1 Nikitin A.

1 2006

1 2004

1 2003

Wyniki wyszukiwania

Solitary wave and other solutions for nonlinear heat equations

Finite dimensional global attractor for a class of doubly nonlinear parabolic equations

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