Abstract
Weak solution (or generalized solution) for the boundary-value problems of partial differential equations of elasticity of 3D (three-dimensional) quasicrystals is given, in which the matrix expression is used. In terms of Korn inequality and theory of function space, we prove the uniqueness of the weak solution. This gives an extension of existence theorem of solution for classical elasticity to that of quasicrystals, and develops the weak solution theory of elasticity of 2D quasicrystals given by the second author of the paper and his students.
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Communicated by YEH Kai-yuan
Project supported by the National Natural Science Foundation of China (Nos. 10372016 and 10672022)
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Guo, Lh., Fan, Ty. Solvability on boundary-value problems of elasticity of three-dimensional quasicrystals. Appl Math Mech 28, 1061–1070 (2007). https://doi.org/10.1007/s10483-007-0808-y
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DOI: https://doi.org/10.1007/s10483-007-0808-y