- Tytuł:
- On the local Cauchy problem for nonlinear hyperbolic functional differential equations
- Autorzy:
- Człapiński, Tomasz
- Powiązania:
- https://bibliotekanauki.pl/articles/1294574.pdf
- Data publikacji:
- 1997
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
functional differential equations
weak solutions
bicharacteristics
successive approximations - Opis:
- We consider the local initial value problem for the hyperbolic partial functional differential equation of the first order (1) $Dₓz(x,y) = f(x,y,z(x,y),(Wz)(x,y),D_y z(x,y))$ on E, (2) z(x,y) = ϕ(x,y) on [-τ₀,0]×[-b,b], where E is the Haar pyramid and τ₀ ∈ ℝ₊, b = (b₁,...,bₙ) ∈ ℝⁿ₊. Using the method of bicharacteristics and the method of successive approximations for a certain functional integral system we prove, under suitable assumptions, a theorem on the local existence of weak solutions of the problem (1),(2).
- Źródło:
-
Annales Polonici Mathematici; 1997, 67, 3; 215-232
0066-2216 - Pojawia się w:
- Annales Polonici Mathematici
- Dostawca treści:
- Biblioteka Nauki
Artykuł