Geodesic
On the mixed problem for quasilinear partial functional differential equations with unbounded delay
Annales Polonici Mathematici, Tome 72 (1999) no. 1, pp. 87-98

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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.
DOI : 10.4064/ap-72-1-87-98
Keywords: Carathéodory solutions, functional differential equation, bicharacteristics, fixed-point theorem, mixed problem, unbounded delay

Tomasz Człapiński 1

1 
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Tomasz Człapiński. On the mixed problem for quasilinear partial functional differential equations with unbounded delay. Annales Polonici Mathematici, Tome 72 (1999) no. 1, pp. 87-98. doi: 10.4064/ap-72-1-87-98

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