Mathematical Framework for Problems of Unbounded Lattices

Abstract

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.

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 2002
Accession Number
ADA411074

Entities

People

  • Benqi Guo

Organizations

  • University of Manitoba

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Applied Mathematics
  • Boundary Value Problems
  • Computational Fluid Dynamics
  • Computational Science
  • Difference Equations
  • Differential Equations
  • Embedding
  • Equations
  • Materials
  • Mathematical Analysis
  • Mathematics
  • Mechanics
  • Partial Differential Equations
  • Periodic Functions
  • Theorems
  • Three Dimensional
  • Variational Equations

Fields of Study

  • Mathematics

Readers

  • Computational Fluid Dynamics (CFD)
  • Linear Algebra

Technology Areas

  • Space