Carathéodory solutions of hyperbolic functional differential inequalities with first order derivatives

• Autorzy: Adrian Karpowicz
• Języki publikacji: EN

Abstrakty

EN

We consider the Darboux problem for a functional differential equation:
$(∂²u)/(∂x∂y) (x,y) = f(x,y,u_{(x,y)},u(x,y),∂u/∂x (x,y),∂u/∂y (x,y))$ a.e. in [0,a]×[0,b],
u(x,y) = ψ(x,y) on [-a₀,a]×[-b₀,b]∖(0,a]×(0,b],
where the function $u_{(x,y)}:[-a₀,0]×[-b₀,0] → ℝ^{k}$ is defined by $u_{(x,y)}(s,t) = u({s+x},{t+y})$ for (s,t) ∈ [-a₀,0]×[-b₀,0]. We give a few theorems about weak and strong inequalities for this problem. We also discuss the case where the right-hand side of the differential equation is linear.

Kategorie tematyczne

• 35L70: Nonlinear second-order hyperbolic equations
• 35R45: Partial differential inequalities
• 35R10: Partial functional-differential equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2008
• Tom: 94
• Numer: 1
• Strony: 53-78

Daty

wydano

2008

Twórcy

autor

Adrian Karpowicz

• Institute of Mathematics, University of Gdańsk, Wit Stwosz St. 57, 80-952 Gdańsk, Poland

Identyfikatory

DOI

10.4064/ap94-1-5