Carathéodory solutions of hyperbolic functional differential inequalities with first order derivatives

Adrian Karpowicz

Annales Polonici Mathematici, Tome 93 (2008), p. 53-78 / Harvested from The Polish Digital Mathematics Library

Résumé

We consider the Darboux problem for a functional differential equation: $(\partial ² u) / (\partial x \partial y) (x, y) = f (x, y, u_{(x, y)}, u (x, y), \partial u / \partial x (x, y), \partial u / \partial y (x, y))$ a.e. in [0,a]×[0,b], u(x,y) = ψ(x,y) on [-a₀,a]×[-b₀,b]∖(0,a]×(0,b], where the function $u_{(x, y)} : [- a ₀, 0] \times [- b ₀, 0] \to ℝ^{k}$ is defined by $u_{(x, y)} (s, t) = u (s + x, t + y)$ for (s,t) ∈ [-a₀,0]×[-b₀,0]. We give a few theorems about weak and strong inequalities for this problem. We also discuss the case where the right-hand side of the differential equation is linear.

Publié le : 2008-01-01

Zbl 1165.35416

EUDML-ID : urn:eudml:doc:281110

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     author = {Adrian Karpowicz},
     title = {Carath\'eodory solutions of hyperbolic functional differential inequalities with first order derivatives},
     journal = {Annales Polonici Mathematici},
     volume = {93},
     year = {2008},
     pages = {53-78},
     zbl = {1165.35416},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap94-1-5}
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Adrian Karpowicz. Carathéodory solutions of hyperbolic functional differential inequalities with first order derivatives. Annales Polonici Mathematici, Tome 93 (2008) pp. 53-78. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap94-1-5/