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1. Quartely international journal on applied analysis, approximation theory, asymptotic analysis, difference equations and more.

2. Through the asymptotic analysis of the crack-tip field, the exponents of singularity of stress and strain in interface static propagating crack-tip field were determined.

3. In this paper, we adopt the asymptotic analysis, get the time inner and outer solution of this model, and this time outer solution approximate the similarity solution.

4. By applying formal asymptotic analysis and Laplace transformation, we obtain two-dimensional model system of linearly viscoelastic "flexural" shell from three-dimensional equations.

5. Chapter 5 focuses on the asymptotic analysis to a parabolic model with inner absorptions and weighted localized sources.

6. By applying formal asymptotic analysis, we obtain two-dimensional model system of linearly dynamic elastic "membrane" and "flexural" shells from three-dimensional equations.

7. On the basis of the governing equations and the asymptotic expansion of the stress fields proposed by Gao and Hwang(http://sentencedict.com/asymptotic analysis.html), a generally asymptotic analysis is performed.

8. The results are analyzed an compared with those calculated by using the asymptotic analysis.

9. The stress and strain singularity exponent of crack-tip field is given by means of the asymptotic analysis.

10. An elastic viscoplastic material model was adopted to the asymptotic analysis on power law and logarithmic singularity of dynamic growing crack tip.

11. The basic method of deriving higher order theories of plates and shells was illustrated by asymptotic analysis for three dimensional thin elastic body.