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Decay and asymptotic behavior of solutions of the Keller-Segel system of degenerate and nondegenerate type

Takayoshi Ogawa (2006)

Banach Center Publications

We classify the global behavior of weak solutions of the Keller-Segel system of degenerate and nondegenerate type. For the stronger degeneracy, the weak solution exists globally in time and has a uniform time decay under some extra conditions. If the degeneracy is weaker, the solution exhibits a finite time blow up if the data is nonnegative. The situation is very similar to the semilinear case. Some additional discussion is also presented.

Decay estimates for solutions of a class of parabolic problems arising in filtration through porous media

G. A. Philippin, S. Vernier-Piro (2001)

Bollettino dell'Unione Matematica Italiana

In questo lavoro si studia un problema di valori al contorno parabolico non lineare che si incontra nello studio dell'infiltrazione di un gas in un mezzo poroso. Si stabiliscono condizioni sui dati che determinano un comportamento di tipo esponenziale decrescente nel tempo per la soluzione e il suo gradiente. Si costruiscono inoltre stime esplicite.

Decay estimates of solutions of a nonlinearly damped semilinear wave equation

Aissa Guesmia, Salim A. Messaoudi (2005)

Annales Polonici Mathematici

We consider an initial boundary value problem for the equation u t t - Δ u - ∇ ϕ · ∇ u + f ( u ) + g ( u t ) = 0 . We first prove local and global existence results under suitable conditions on f and g. Then we show that weak solutions decay either algebraically or exponentially depending on the rate of growth of g. This result improves and includes earlier decay results established by the authors.

Decay of covariances, uniqueness of ergodic component and scaling limit for a class of ∇ φ systems with non-convex potential

Codina Cotar, Jean-Dominique Deuschel (2012)

Annales de l'I.H.P. Probabilités et statistiques

We consider a gradient interface model on the lattice with interaction potential which is a non-convex perturbation of a convex potential. Using a technique which decouples the neighboring vertices into even and odd vertices, we show for a class of non-convex potentials: the uniqueness of ergodic component for ∇ φ -Gibbs measures, the decay of covariances, the scaling limit and the strict convexity of the surface tension.

Decay of solutions of some degenerate hyperbolic equations of Kirchhoff type

Barbara Szomolay (2003)

Commentationes Mathematicae Universitatis Carolinae

In this paper we study the asymptotic behavior of solutions to the damped, nonlinear vibration equation with self-interaction u ¨ = - γ u ˙ + m ( ∥ ∇ u ∥ 2 ) Δ u - δ | u | α u + f , which is known as degenerate if m ( · ) ≥ 0 , and non-degenerate if m ( · ) ≥ m 0 > 0 . We would like to point out that, to the author’s knowledge, exponential decay for this type of equations has been studied just for the special cases of α . Our aim is to extend the validity of previous results in [5] to α ≥ 0 both to the degenerate and non-degenerate cases of m . We extend our results to equations with...

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