Annales Mathematiques Africaines


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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.

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