A transmission problem for thermoelastic plates

Abstract

Abstract.In this paper we study a transmission problem for thermoelastic plates. We prove that the problem is well-posed in the sense that there exists only one solution which is as regular as the initial data. Moreover, we prove that the local thermal effect is strong enough to produce uniform rate of decay of the solution. More precisely, there exist positive constants C and 7 such that the total energy E(t) satisfies E(t) < CE{0)e"7t.

The global solvability and asymptotic behavior of a transmission problem for Kirchhoff‐type wave equations with memory source on the boundary

“…For the transmission problem, we can see previous works for the studies of existence, regularity, controllability, and decay estimate of solutions for the transmission problem with Laplacian operators. For example, Marzocchi proved that the solution for a one‐dimensional space of a semilinear transmission problem between an elastic and thermoelastic material decays exponentially.…”

One spatial variable thermoelastic transmission problem in viscoelasticity located in the second part

“…The stability of various transmission problems on thermoelasticity have been considered . The transmission problem to hyperbolic equations was studied by Dautray and Lions, where the existence and regularity of solutions for the linear problem have been proved.…”

“…The transmission problem to hyperbolic equations was studied by Dautray and Lions, where the existence and regularity of solutions for the linear problem have been proved. In the work of Muñoz and Oquendo, the authors considered the transmission problem of viscoelastic waves satisfying boundary conditions and initial conditions. The authors studied the wave propagations over materials consisting of elastic and viscoelastic components.…”

Nonlinear Transmission Problem for Wave Equation with Boundary Condition of Memory Type

“…We note that problems (1.1)-(1.6) are related to the stationary problem of two wave equations of Kirchhoff type, which models the transverse vibrations of the membrane composed by two different materials in Ω 1 and Ω 2 . For the transmission problem, see [5][6][7]9]. Marzocchi [6] proved that the solution for a one-dimensional space of a semilinear transmission problem between an elastic and thermoelastic material decays exponentially to zero.…”

“…Our work was motivated by the ones of Rivera [9] and Andrade [1]. Rivera [9] considered the following transmission problem of viscoelastic waves of the form:…”