Dissertação
Existência, unicidade e estabilidade de solução para um problema termoelástico hiperbólico com domínio não limitado em R
Fecha
2019-08-29Autor
Pieper, Christian Róger Vilela
Institución
Resumen
Consider the Cauchy Problem which describes the dynamics of linear
rafters vibrations in R subjected to thermal e ects modeled by the Cattaneo
law.
We will focus our attention on obtaining the existence and uniqueness
of the solution and analyzing the asymptotic behavior of such a solution.
In the rst part we will prove the existence and uniqueness of solutions
for the thermoelastic model.
8>
><>>:
utt + uxxxx ����� uxxtt + xx = 0; em R [0;+1)
t + kqx ����� uxxt = 0; em R [0;+1)
qt + q + k x = 0; em R [0;+1)
:
With initial conditions u(x; 0) = u0(x); ut(x; 0) = u1(x); (x; 0) = 0(x);
q(x; 0) = q0(x):
In the second part we nd a decay rate for total energy
E(t) =
1
2 ZR u2
t + u2
tx + u2
xx + 2 + q2 dx
associated with the model described above.