# Carathéodory solutions of hyperbolic functional differential inequalities with first order derivatives

Annales Polonici Mathematici (2008)

- Volume: 94, Issue: 1, page 53-78
- ISSN: 0066-2216

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topAdrian Karpowicz. "Carathéodory solutions of hyperbolic functional differential inequalities with first order derivatives." Annales Polonici Mathematici 94.1 (2008): 53-78. <http://eudml.org/doc/281110>.

@article{AdrianKarpowicz2008,

abstract = {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.},

author = {Adrian Karpowicz},

journal = {Annales Polonici Mathematici},

keywords = {functional differential inequalities; hyperbolic equations; Darboux problem; solutions in the sense of Carathéodory},

language = {eng},

number = {1},

pages = {53-78},

title = {Carathéodory solutions of hyperbolic functional differential inequalities with first order derivatives},

url = {http://eudml.org/doc/281110},

volume = {94},

year = {2008},

}

TY - JOUR

AU - Adrian Karpowicz

TI - Carathéodory solutions of hyperbolic functional differential inequalities with first order derivatives

JO - Annales Polonici Mathematici

PY - 2008

VL - 94

IS - 1

SP - 53

EP - 78

AB - 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.

LA - eng

KW - functional differential inequalities; hyperbolic equations; Darboux problem; solutions in the sense of Carathéodory

UR - http://eudml.org/doc/281110

ER -

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