We consider the local initial value problem for the hyperbolic partial functional differential equation of the first order (1) 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).
@article{bwmeta1.element.bwnjournal-article-apmv67z3p215bwm,
author = {Tomasz Cz\l api\'nski},
title = {On the local Cauchy problem for nonlinear hyperbolic functional differential equations},
journal = {Annales Polonici Mathematici},
volume = {66},
year = {1997},
pages = {215-232},
zbl = {0899.35121},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv67z3p215bwm}
}
Tomasz Człapiński. On the local Cauchy problem for nonlinear hyperbolic functional differential equations. Annales Polonici Mathematici, Tome 66 (1997) pp. 215-232. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv67z3p215bwm/
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