Displaying similar documents to “Approximation methods for solving the Cauchy problem”

Moment sequences and abstract Cauchy problems

Claus Müller (2003)

Commentationes Mathematicae Universitatis Carolinae

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We give a new characterization of the solvability of an abstract Cauchy problems in terms of moment sequences, using the resolvent operator at only one point.

Local Lipschitz continuity of the stop operator

Wolfgang Desch (1998)

Applications of Mathematics

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On a closed convex set Z in N with sufficiently smooth ( 𝒲 2 , ) boundary, the stop operator is locally Lipschitz continuous from 𝐖 1 , 1 ( [ 0 , T ] , N ) × Z into 𝐖 1 , 1 ( [ 0 , T ] , N ) . The smoothness of the boundary is essential: A counterexample shows that 𝒞 1 -smoothness is not sufficient.

The Cauchy problem for systems through the normal form of systems and theory of weighted determinant

Waichiro Matsumoto (1998-1999)

Séminaire Équations aux dérivées partielles

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The author propose what is the principal part of linear systems of partial differential equations in the Cauchy problem through the normal form of systems in the meromorphic formal symbol class and the theory of weighted determinant. As applications, he choose the necessary and sufficient conditions for the analytic well-posedness ( Cauchy-Kowalevskaya theorem ) and C well-posedness (Levi condition).

Abstract version of the Cauchy-Kowalewski problem

Oleg Zubelevich (2004)

Open Mathematics

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We consider an abstract version of the Cauchy-Kowalewski Problem with the right hand side being free from the Lipschitz type conditions and prove the existence theorem.