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

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Człapiński T.

Annales Polonici Mathematici

1999

tom 72

nr 1

87-98

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.

Ograniczanie wyników

1 Annales Polonici Mathematici

1 Człapiński T.

1 1999

Wyniki wyszukiwania

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