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Redlinger, Reinhard

Existence theorems for semilinear parabolic systems with functionals. (English) Zbl 0543.35052

Nonlinear Anal., Theory Methods Appl. 8, 667-682 (1984).
On considère des systèmes d’équations différentielles partielles semi-linéaires de la forme \(L(u)=f(t,x,u(\cdot)),\) avec des conditions au bord soit \(u_ k=0\) soit \(\partial u_ k/\partial \nu_ k=g_ k(t,x,u(\cdot))\) 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

Cited in 47 Documents

MSC:

35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35D05 Existence of generalized solutions of PDE (MSC2000)

Keywords:

parabolic systems with functionals; lower and upper solutions; semi- linear equation; potential; uniformly parabolic; existence
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\textit{R. Redlinger}, Nonlinear Anal., Theory Methods Appl. 8, 667--682 (1984; Zbl 0543.35052)
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