Displaying similar documents to “Existence of solution for a mixed neutral system.”

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.

Mixed 3-Sasakian structures and curvature

Angelo V. Caldarella, Anna Maria Pastore (2009)

Annales Polonici Mathematici

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We deal with two classes of mixed metric 3-structures, namely the mixed 3-Sasakian structures and the mixed metric 3-contact structures. First, we study some properties of the curvature of mixed 3-Sasakian structures. Then we prove the identity between the class of mixed 3-Sasakian structures and the class of mixed metric 3-contact structures.

Instability of mixed finite elements for Richards' equation

Březina, Jan

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Richards' equation is a widely used model of partially saturated flow in a porous medium. In order to obtain conservative velocity field several authors proposed to use mixed or mixed-hybrid schemes to solve the equation. In this paper, we shall analyze the mixed scheme on 1D domain and we show that it violates the discrete maximum principle which leads to catastrophic oscillations in the solution.