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Existence theorems for semilinear parabolic systems with functionals. (English) Zbl 0543.35052
On considère des systèmes d’équations différentielles partielles semi-linéaires de la forme L(u)=f(t,x,u(·)), avec des conditions au bord soit u k =0 soit u k /ν k =g k (t,x,u(·)) ou u=(u 1 ,u 2 ,···,u N )· L’opérateur L est linéaire uniformément parabolique. L’auteur met en évidence de bonnes hypothèses sur les non-linéarités pour obtenir, grâce à des potentiels bien choisis et à des théorèmes de point fixe, des théorèmes d’existence de solutions des problèmes posés, en un sens faible et fort.
Reviewer: M.-T.Lacroix
35K60Nonlinear initial value problems for linear parabolic equations
35A05General existence and uniqueness theorems (PDE) (MSC2000)
35D05Existence of generalized solutions of PDE (MSC2000)