We look at the Cauchy problem with an accretive Operator on a Banach space.
We give an upper bound for the norm of the difference of two solutions of Euler schemes with this accretive operator. This concrete estimate also works for the problem with a non-zero right-hand side in the Cauchy problem and is a generalization of a famous result by Kobayashi.
We also show, how this result gives direct proofs for existence, uniqueness, stability and regularity of Euler solutions of the Cauchy problem and also the rate of convergence of solutions of Euler schemes.
The results concerning regularity and rate of convergence are generalized for problem data in interpolation sets.:1. Accretive operators
1.1. Thebracket.
1.2. Accretive operators
1.3. The Cauchy problem and Euler solutions
2. A priori estimates for solutions of implicit Euler schemes
2.1. An implicit upper bound
2.2. Properties of the density
2.3. An explicit upper bound
3. Applications
3.1. Wellposedness of the Cauchy problem
3.2. Interpolation theory
A. Functions of bounded variation
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:89151 |
| Date | 06 February 2024 |
| Creators | Beurich, Johann Carl |
| Contributors | Chill, Ralph, Warma, Mahamadi, Technische Universität Dresden |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | info:eu-repo/semantics/publishedVersion, doc-type:doctoralThesis, info:eu-repo/semantics/doctoralThesis, doc-type:Text |
| Rights | info:eu-repo/semantics/openAccess |
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