Decay Rates of Solutions for the Magneto-thermo-elastic System in R3


Curso alvo : Matemática Aplicada a Negócios

Palestrante : Prof. Dr. Cleverson Roberto da Luz

Data: 09/02/2017

Hora de ínicio: 16:00:00
Hora de término: 17:00:00
Local: Laboratório de Informática 602


In our discussionwe consider the following evolution system describing anmagneto-thermoelastic
phenomenon in R3:
ut t ÅL(u)Å®ut Å°rµ Æ curlh £H,
ht ź1 curlcurlh Æ curl(ut £H),
µt ¡·¢µÅ°divut Æ 0, (0.1)
divh Æ 0,
u(0,x) Æ u0(x), ut (0,x) Æ u1(x),
h(0,x) Æ h0(x), µ(0,x) Æ µ0(x),
for all (t ,x) 2 RÅ £R3, where L(u) Æ ¡¹¢u ¡(¸Å¹)rdivu with positive constants ¸,¹. In
the above system we denote by u Æ (u1,u2,u3) the displacement vector, h Æ (h1,h2,h3) the
magnetic induction and µ is the temperature difference with respect to a fixed reference
temperature. The coupling constants ¹0 (magnetic permeability) and ° are positive and
H Æ (0, 0,1) Æ e3 denotes the constant external magnetic field. The remaining constant
º1 is defined as 1/(¾¹0), where ¾ È 0 is the conductivity of the material. In this work we
study the asymptotic behavior of solutions for to problem (1). We improve results on decay
rates considering weaker regularity on the initial data when compared to previous works in
the literature. We also improve the method developed in [1], extending it for this coupled
system of mixed hyperbolic-parabolic partial differential equations.

Resumo: 170_abstractcleverson.pdf

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