The existence of Carathéodory solutions of hyperbolic functional differential equations

• Autorzy: Adrian Karpowicz
• Języki publikacji: EN

Abstrakty

EN

We consider the following Darboux problem for the functional differential equation
$∂²u/∂x∂y(x,y) = f(x,y,u_{(x,y)},∂u/∂x(x,y),∂u/∂y(x,y))$ 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 prove a theorem on existence of the Carathéodory solutions of the above problem.

Słowa kluczowe

EN

existence theorem; functional differential equation; hyperbolic equation; Darboux problem; solution in the sense of Carathéodory

Kategorie tematyczne

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

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae, Differential Inclusions, Control and Optimization
• Rocznik: 2010
• Tom: 30
• Numer: 1
• Strony: 121-140

Daty

wydano

2010

otrzymano

2009-06-20

Twórcy

autor

Adrian Karpowicz

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

Bibliografia

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Identyfikatory

DOI

10.7151/dmdico.1115