Mathematical Framework for Problems of Unbounded Lattices
Final rept. 25 May 1999-24 May 2002
MANITOBA UNIV WINNIPEG DEPT OF MATHEMATICS
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This final progress report summarizes the progresses of our research in the period 1999-2002. Starting with problems of periodic lattices in entire spaces, and we focus on the mathematical framework for problems of unstructured lattice in unbounded domains without absolute terms. In this framework, the existence and uniqueness of solution for the problem without absolute terms in entire and half spaces Rd and Rd, d 1, 2, 3 are proved in energy spaces. For unstructured lattices, new methodology and approach have been developed successfully, i.e. extension of grid functions by linear interpolation, which is essential to the some embedding results in discrete Sobolev spaces. These embeddings lead to the proof of existence of solutions.
- Laminates and Composite Materials
- Numerical Mathematics