Existence and decay in non linear viscoelasticity

Jaime E. Muñoz Rivera; Félix P. Quispe Gómez

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 $ℜ α$ . 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 $|α| < C ℜ α$ , dove $C$ dipende da $K$ e $N$ .

On the $L_{p}$ -decay and local energy decay of solutions to nonlinear Klein-Gordon equations

Philip Brenner (2003)

Banach Center Publications

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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 $u_{t t} - Δ u - \nabla ϕ \cdot \nabla u + f (u) + g (u_{t}) = 0$ . 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.

Global existence and $L_{p}$ decay estimate of solution for Cahn-Hilliard equation with inertial term

Hongmei Xu, Qi Li (2021)

Applications of Mathematics

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The Cauchy problem of the Cahn-Hilliard equation with inertial term in multi space dimension is considered. Based on detailed analysis of Green’s function, using fixed-point theorem, we get the global existence in time of classical solution with large initial data. Furthermore, we get $L_{p}$ decay rate of the solution.

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 $+\infty$ (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 $- div (Q^{ϵ} G (x, N^{ϵ} \nabla u)) = f^{ϵ},$ 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, $1 < p < \infty$ , 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 $\begin{matrix} f (x, η, ξ) \geq a (x) \frac{{| ξ |}^{p}}{{(1 + | η |)}^{α}} - b_{1} (x) {| η |}^{β_{1}} - g_{1} (x), \\ f (x, η, 0) \leq b_{2} (x) {| η |}^{β_{2}} + g_{2} (x), \end{matrix}$ where $0 \leq α < p$ , $1 \leq β_{1} < p$ , $0 \leq β_{2} < p$ , $α + β_{i} \leq p$ , $a (x)$ , $b_{i} (x)$ , $g_{i} (x)$ ( $i = 1$ , $2$ ) 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 $u_{0} \in W^{1, p} (a) \cap L^{\infty} (Ω)$ .

On the radius of spatial analyticity for the higher order nonlinear dispersive equation

Aissa Boukarou, Kaddour Guerbati, Khaled Zennir (2022)

Mathematica Bohemica

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In this work, using bilinear estimates in Bourgain type spaces, we prove the local existence of a solution to a higher order nonlinear dispersive equation on the line for analytic initial data $u_{0}$ . The analytic initial data can be extended as holomorphic functions in a strip around the $x$ -axis. By Gevrey approximate conservation law, we prove the existence of the global solutions, which improve earlier results of Z. Zhang, Z. Liu, M. Sun, S. Li, (2019).