- Tytuł:
- Classical solutions of hyperbolic partial differential equations with implicit mixed derivative
- Autorzy:
- Marano, Salvatore
- Powiązania:
- https://bibliotekanauki.pl/articles/1312194.pdf
- Data publikacji:
- 1992
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
hyperbolic equation
implicit mixed derivative
classical solution - Opis:
-
Let f be a continuous function from $[0,a] × [0,β] × (ℝ^n)⁴$ into $ℝ^n$. Given $u₀,v₀ ∈ C⁰([0,β],ℝ^n)$, with
f(0, x, ∫_0^x u₀(s)ds, ∫_0^x v₀(s)ds, u₀(x), v₀(x)) = v₀(x)
for every x ∈ [0,β], consider the problem
(P) { ∂²z/(∂t∂x) = f(t, x, z, ∂z/∂t, ∂z/∂x, ∂²z/(∂t∂x)),
$z(t,0) = ϑ_{ℝ^n}$, $z(0,x)=∫_0^x u₀(s)ds$, ∂²z(0,x)/(∂t∂x) = v₀(x). In this paper we prove that, under suitable assumptions, problem (P) has at least one classical solution that is local in the first variable and global in the other. As a consequence, we obtain a generalization of a result by P. Hartman and A. Wintner ([4], Theorem 1). - Źródło:
-
Annales Polonici Mathematici; 1991-1992, 56, 2; 163-178
0066-2216 - Pojawia się w:
- Annales Polonici Mathematici
- Dostawca treści:
- Biblioteka Nauki
Artykuł