Nonexistence results for the Cauchy problem of some systems of hyperbolic equations

• Autorzy: Mokhtar Kirane , Salim Messaoudi
• Języki publikacji: EN

Abstrakty

EN

We consider the systems of hyperbolic equations
⎧$uₜₜ = Δ(a(t,x)u) + Δ(b(t,x)v) + h(t,x)|v|^{p}$, t > 0, $x ∈ ℝ^{N}$, (S1)
⎨
⎩$vₜₜ = Δ(c(t,x)v) + k(t,x)|u|^{q}$, t > 0, $x ∈ ℝ^{N}$
⎧$uₜₜ = Δ(a(t,x)u) + h(t,x)|v|^{p}$, t > 0, $x ∈ ℝ^{N}$, (S2)
⎨
⎩$vₜₜ = Δ(c(t,x)v) + l(t,x)|v|^{m} + k(t,x)|u|^{q}$, t > 0, $x ∈ ℝ^{N}$, (S3)
⎧$uₜₜ = Δ(a(t,x)u) + Δ(b(t,x)v) + h(t,x)|u|^{p}$, t > 0, $x ∈ ℝ^{N}$,
⎨
⎩$vₜₜ = Δ(c(t,x)v) + k(t,x)|v|^{q}$, t > 0, $x ∈ ℝ^{N}$,
in $(0,∞) × ℝ^{N}$ with u(0,x) = u₀(x), v(0,x) = v₀(x), uₜ(0,x) = u₁(x), vₜ(0,x) = v₁(x). We show that, in each case, there exists a bound B on N such that for 1 ≤ N ≤ B solutions to the systems blow up in finite time.

Kategorie tematyczne

• 35L70: Nonlinear second-order hyperbolic equations
• 35L15: Initial value problems for second-order hyperbolic equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2002
• Tom: 78
• Numer: 1
• Strony: 39-47

Daty

wydano

2002

Twórcy

autor

Mokhtar Kirane

• Université de Picardie Jules Verne, Faculté de Mathématiques, et d'Informatique, LAMFA UPRES, A 6119, 33 rue Saint Leu, 80039 Amiens Cedex 1, France

autor

Salim Messaoudi

• Department of Mathematical Sciences, King Fahd University, of Petroleum and Minerals, Dhahran 31261, Saudi Arabia

Identyfikatory

DOI

10.4064/ap78-1-5