On the mixed problem for quasilinear partial functional differential equations with unbounded delay

• Autorzy: Tomasz Człapiński
• Języki publikacji: EN

Abstrakty

EN

We consider the mixed problem for the quasilinear partial functional differential equation with unbounded delay
$D_tz(t,x) = ∑_{i=1}^n f_i(t,x,z_{(t,x)})D_{x_i}z(t,x) + h(t,x,z_{(t,x)})$,
where $z_{(t,x)} ∈ X̶_0$ is defined by $z_{(t,x)}(τ,s) = z(t+τ,x+s)$, $(τ,s) ∈ (-∞,0]×[0,r]$, and the phase space $X̶_0$ satisfies suitable axioms. Using the method of bicharacteristics and the fixed-point method we prove a theorem on the local existence and uniqueness of Carathéodory solutions of the mixed problem.

Słowa kluczowe

EN

Carathéodory solutions; functional differential equation; bicharacteristics; fixed-point theorem; mixed problem; unbounded delay

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1999
• Tom: 72
• Numer: 1
• Strony: 87-98

Daty

wydano

1999

otrzymano

1998-11-18

Twórcy

autor

Tomasz Człapiński

• Institute of Mathematics, University of Gdańsk, Wita Stwosza 57, 80-952 Gdańsk, Poland

Bibliografia

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