Classical solutions of initial problems for quasilinear partial functional differential equations of the first order

• Autorzy: Czernous W.
• Języki publikacji: EN

Abstrakty

EN

We consider the initial problem for a quasilinear partial functional differential equation of the first order [formula], z(t, x) = varphi(t, x) ((t, x) ∈ [-h0, 0] x Rn) where z(t, x) : [-h0, 0] x [-h, h] → R is a function defined by z(t, x) (τ, ξ) = z(t + τ, + ξ) for (τ, ξ) ∈ [-h0, 0] x [-h, h]. Using the method of bicharacteristics and the fixed-point theorem we prove, under suitable assumptions, a theorem on the local existence and uniqueness of classical solutions of the problem and its continuous dependence on the initial condition.

Słowa kluczowe

EN

partial functional differential equations; classical solutions; local existence; bicharacteristics

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2006
• Tom: Vol. 26, no. 1
• Strony: 13--29
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Czernous W.

• University of Gdańsk, Institute of Mathematics, Wit Stwosz Street 57, 80-952 Gdańsk, Poland,

Bibliografia

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