Displaying similar documents to “Existence and decay in non linear viscoelasticity”

Global existence and regularity of solutions for complex Ginzburg-Landau equations

Stéphane Descombes, Mohand Moussaoui (2000)

Bollettino dell'Unione Matematica Italiana

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Si considerano equazioni di Ginzburg-Landau complesse del tipo u t - α Δ u + P u 2 u = 0 in R N dove P è polinomio di grado K a coefficienti complessi e α è un numero complesso con parte reale positiva α . Nell'ipotesi che la parte reale del coefficiente del termine di grado massimo P sia positiva, si dimostra l'esistenza e la regolarità di una soluzione globale nel caso α < C α , dove C dipende da K e N .

Decay estimates of solutions of a nonlinearly damped semilinear wave equation

Aissa Guesmia, Salim A. Messaoudi (2005)

Annales Polonici Mathematici

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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.

The Landau-Lifshitz equations and the damping parameter

K. Hamdache, M. Tilioua (2006)

Bollettino dell'Unione Matematica Italiana

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The present paper is particularly devoted to the damping effect in ferromagnetic materials. We are interested in determining the sensitivity of the LLG method solution to the phenomenological damping parameter a. We discuss the behaviour of the global weak solutions with finite energy of the Landau-Lifshitz equations when the damping parameter a tends either to 0 (underdamped case) or + (overdamped case).

Homogenization of some nonlinear problems with specific dependence upon coordinates

P. Courilleau, S. Fabre, J. Mossino (2001)

Bollettino dell'Unione Matematica Italiana

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Questo articolo considera una successione di equazioni differenziali a derivate parziali non lineari in forma di divergenza del tipo - div Q ϵ G x , N ϵ u = f ϵ , in un dominio limitato Ω dello spazio n -dimensionale; Q ϵ = Q ϵ x e N ϵ = N ϵ x sono matrici con coefficenti limitati, N ϵ e è invertibile e la sua matrice inversa R ϵ ha anche coefficenti limitati. La non linearità è dovuta alla funzione G = G x , ξ ; la condizione di crescita, la monotonicità e le ipotesi di coercitività sono modellate sul p -Laplaciano, 1 < p < , ed assicurano l'esistenza di...

Existence and boundedness of minimizers of a class of integral functionals

A. Mercaldo (2003)

Bollettino dell'Unione Matematica Italiana

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In this paper we consider a class of integral functionals whose integrand satisfies growth conditions of the type f ( x , η , ξ ) a ( x ) | ξ | p ( 1 + | η | ) α - b 1 ( x ) | η | β 1 - g 1 ( x ) , f ( x , η , 0 ) b 2 ( x ) | η | β 2 + g 2 ( x ) , where 0 α < p , 1 β 1 < p , 0 β 2 < p , α + β i p , a x , b i x , g i x ( i = 1 , 2 ) are nonnegative functions satisfying suitable summability assumptions. We prove the existence and boundedness of minimizers of such a functional in the class of functions belonging to the weighted Sobolev space W 1 , p a , which assume a boundary datum u 0 W 1 , p a L Ω .

Partial Hölder continuity results for solutions of non linear non variational elliptic systems with limit controlled growth

Luisa Fattorusso, Giovanna Idone (2002)

Bollettino dell'Unione Matematica Italiana

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Let Ω be a bounded open subset of R n , n > 4 , of class C 2 . Let u H 2 Ω a solution of elliptic non linear non variational system a x , u , D u , H u = b x , u , D u where a x , u , μ , ξ and b x , u , μ are vectors in R N , N 1 , measurable in x , continuous in u , μ , ξ and u , μ respectively. Here, we demonstrate that if b x , u , μ has limit controlled growth, if a x , u , μ , ξ is of class C 1 in ξ and satisfies the Campanato condition A and, together with a ξ , certain continuity assumptions, then the vector D u is partially Hölder continuous for every exponent α < 1 - n p .

Large data local solutions for the derivative NLS equation

Ioan Bejenaru, Daniel Tataru (2008)

Journal of the European Mathematical Society

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We consider the derivative NLS equation with general quadratic nonlinearities. In [2] the first author has proved a sharp small data local well-posedness result in Sobolev spaces with a decay structure at infinity in dimension n = 2 . Here we prove a similar result for large initial data in all dimensions n 2 .