On the local Cauchy problem for nonlinear hyperbolic functional differential equations

Volume 67 / 1997

Tomasz Człapiński Annales Polonici Mathematici 67 (1997), 215-232 DOI: 10.4064/ap-67-3-215-232


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).


  • Tomasz Człapiński

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