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Exponential decay to partially thermoelastic materials

Jaime E. Muñoz Rivera, Vanilde Bisognin, Eleni Bisognin (2002)

Bollettino dell'Unione Matematica Italiana

We study the thermoelastic system for material which are partially thermoelastic. That is, a material divided into two parts, one of them a good conductor of heat, so there exists a thermoelastic phenomenon. The other is a bad conductor of heat so there is not heat flux. We prove for such models that the solution decays exponentially as time goes to infinity. We also consider a nonlinear case.

Exponential stability for Timoshenko model with thermal effect

Luiz Gutemberg Rosário Miranda, Bruno Magalhães Alves (2025)

Applications of Mathematics

We performe an exponential decay analysis for a Timoshenko-type system under the thermal effect by constructing the Lyapunov functional. More precisely, this thermal effect is acting as a mechanism for dissipating energy generated by the bending of the beam, acting only on the vertical displacement equation, different from other works already existing in the literature. Furthermore, we show the good placement of the problem using semigroup theory.

Exponential stability of a flexible structure with history and thermal effect

Roberto Díaz, Jaime Muñoz, Carlos Martínez, Octavio Vera (2020)

Applications of Mathematics

In this paper we study the asymptotic behavior of a system composed of an integro-partial differential equation that models the longitudinal oscillation of a beam with a memory effect to which a thermal effect has been given by the Green-Naghdi model type III, being physically more accurate than the Fourier and Cattaneo models. To achieve this goal, we will use arguments from spectral theory, considering a suitable hypothesis of smoothness on the integro-partial differential equation.

Extension and lacunas of solutions of linear partial differential equations

Uwe Franken, Reinhold Meise (1996)

Annales de l'institut Fourier

Let K ⊂ Q be compact, convex sets in ℝ n with K ∘ ≠ ∅ and let P ( D ) be a linear, constant coefficient PDO. It is characterized in various ways when each zero solution of P ( D ) in the space ℰ ( K ) of all C ∞ -functions on K extends to a zero solution in ℰ ( Q ) resp. in ℰ ( ℝ n ) . The most relevant characterizations are in terms of Phragmén-Lindelöf conditions on the zero variety of P in ℂ n and in terms of fundamental solutions for P ( D ) with lacunas.

Extension of a regularity result concerning the dam problem

Gianni Gilardi, Stephan Luckhaus (1991)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

One proves, in the case of piecewise smooth coefficients, that the time derivative of the solution of the so called dam problem is a measure, extending the result proved by the same authors in the case of Lipschitz continuous coefficients.

Extension of Díaz-Saá's inequality in RN and application to a system of p-Laplacian.

Karim Chaïb (2002)

Publicacions Matemàtiques

The purpose of this paper is to extend the Díaz-Saá’s inequality for the unbounded domains as RN.The proof is based on the Picone’s identity which is very useful in problems involving p-Laplacian. In a second part, we study some properties of the first eigenvalue for a system of p-Laplacian. We use Díaz-Saá’s inequality to prove uniqueness and Egorov’s theorem for the isolation. These results generalize J. Fleckinger, R. F. Manásevich, N. M. Stavrakakis and F. de Thélin’s work [9] for the first...

Currently displaying 341 – 360 of 366