Geodesic
On the local Cauchy problem for nonlinear hyperbolic functional differential equations
Annales Polonici Mathematici, Tome 67 (1997) no. 3, pp. 215-232.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We consider the local initial value problem for the hyperbolic partial functional differential equation of the first order (1) $Dₓz(x,y) = f(x,y,z(x,y),(Wz)(x,y),D_y z(x,y))$ on E, (2) z(x,y) = ϕ(x,y) on [-τ₀,0]×[-b,b], where E is the Haar pyramid and τ₀ ∈ ℝ₊, b = (b₁,...,bₙ) ∈ ℝⁿ₊. Using the method of bicharacteristics and the method of successive approximations for a certain functional integral system we prove, under suitable assumptions, a theorem on the local existence of weak solutions of the problem (1),(2).
DOI : 10.4064/ap-67-3-215-232
Keywords: functional differential equations, weak solutions, bicharacteristics, successive approximations

Tomasz Człapiński 1

1 
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Tomasz Człapiński. On the local Cauchy problem for nonlinear hyperbolic functional differential equations. Annales Polonici Mathematici, Tome 67 (1997) no. 3, pp. 215-232. doi : 10.4064/ap-67-3-215-232. http://geodesic.mathdoc.fr/articles/10.4064/ap-67-3-215-232/

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