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Problème initial et aux limites avec une condition non locale pour une équation pseudoparabolique de transfert d’humidité de troisième ordre

N’gniamessan GBENOUGA
06BP : 62337 Lomé Togo

Aboudou-Fataou MOROU, Mawussi TODJRO and Kokou TCHARIE
BP : 1515 Lomé Togo

Mathematics Subject Classification: (2010) 35K70, 35A35, 34A12
Key words: pseudoparabolic equations, a priori energetic inequality, continuous dependence

Abstract:

In the rectangle O = (0,l) × (0,T), consider the equation :

( 2 ) ( ) L ?v = ?v- ? ?-- b(x,t) ?-v- - -?- a(x,t)?v- = f1(x,t) (1.1) ?t ?x ?x?t ?x ?x

with initial condition

Lv = v(x,t)|t=0 = f1(x), x ? (0,l), (1.2)

and Dirichlet or Neumann condition on x = 0

?v v(x,t)|x=0 = h(t), or --(x,t)|x=0 = g(t),t ? [0;T ] (1.3) ?x

and also integral condition

? l a v(x,t)dx = µ(t), 0 = a < l, t ? [0,T] (1.4)

where λ is a positive real parameter and a(x,t), b(x,t), f₁(x,t), f₁(x), µ(t), h(t) and g(t) are known functions that satisfy well-defined conditions.

We establishe the a priori energetic inequality which guarantees the uniqueness of the solution and show the continuous dependance of the solution to the parameter λ.