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Displaying similar documents to “On the limits of solutions of functional differential equations”

On the mixed problem for quasilinear partial functional differential equations with unbounded delay

Tomasz Człapiński (1999)

Annales Polonici Mathematici

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We consider the mixed problem for the quasilinear partial functional differential equation with unbounded delay D t z ( t , x ) = i = 1 n f i ( t , x , z ( t , x ) ) D x i z ( t , x ) + h ( t , x , z ( t , x ) ) , where z ( t , x ) X ̶ 0 is defined by z ( t , x ) ( τ , s ) = z ( t + τ , x + s ) , ( τ , s ) ( - , 0 ] × [ 0 , r ] , and the phase space X ̶ 0 satisfies suitable axioms. Using the method of bicharacteristics and the fixed-point method we prove a theorem on the local existence and uniqueness of Carathéodory solutions of the mixed problem.