On the local Cauchy problem for nonlinear hyperbolic functional differential equations
Annales Polonici Mathematici, Tome 67 (1997) no. 3, pp. 215-232
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).
Keywords:
functional differential equations, weak solutions, bicharacteristics, successive approximations
@article{10_4064_ap_67_3_215_232,
author = {Tomasz Cz{\l}api\'nski},
title = {On the local {Cauchy} problem for nonlinear hyperbolic functional differential equations},
journal = {Annales Polonici Mathematici},
pages = {215--232},
year = {1997},
volume = {67},
number = {3},
doi = {10.4064/ap-67-3-215-232},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/ap-67-3-215-232/}
}
TY - JOUR AU - Tomasz Człapiński TI - On the local Cauchy problem for nonlinear hyperbolic functional differential equations JO - Annales Polonici Mathematici PY - 1997 SP - 215 EP - 232 VL - 67 IS - 3 UR - http://geodesic.mathdoc.fr/articles/10.4064/ap-67-3-215-232/ DO - 10.4064/ap-67-3-215-232 LA - en ID - 10_4064_ap_67_3_215_232 ER -
%0 Journal Article %A Tomasz Człapiński %T On the local Cauchy problem for nonlinear hyperbolic functional differential equations %J Annales Polonici Mathematici %D 1997 %P 215-232 %V 67 %N 3 %U http://geodesic.mathdoc.fr/articles/10.4064/ap-67-3-215-232/ %R 10.4064/ap-67-3-215-232 %G en %F 10_4064_ap_67_3_215_232
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
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