- Tytuł:
- On the mixed problem for quasilinear partial functional differential equations with unbounded delay
- Autorzy:
- Człapiński, Tomasz
- Powiązania:
- https://bibliotekanauki.pl/articles/1294042.pdf
- Data publikacji:
- 1999
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
Carathéodory solutions
functional differential equation
bicharacteristics
fixed-point theorem
mixed problem
unbounded delay - Opis:
- 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.
- Źródło:
-
Annales Polonici Mathematici; 1999, 72, 1; 87-98
0066-2216 - Pojawia się w:
- Annales Polonici Mathematici
- Dostawca treści:
- Biblioteka Nauki
Artykuł