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Phase transitions via bifurcation from heteroclinic orbits. (English) Zbl 0532.73082

Systems of nonlinear partial differential equations, Proc. NATO Adv. Study Inst., Oxford/U.K. 1982, NATO ASI Ser. C 111, 333-341 (1983).
[For the entire collection see Zbl 0514.00014.]
The paper poses a problem of the variational calculus, arising in the stretching of a thin elastic bar by end forces, and tries to find the unknown function by expressing it as an Euler-Lagrange equation. The details of calculations are not given, even though the problem is a quite mathematical one. The results are presented and are shown in graphical forms. Not much emphasis is put on the physical aspects, even though the problem arises from the practical considerations. However, the paper may be useful to those interested in the theory of the nonlinear differential equations.
Reviewer: G.Paria

MSC:

74P99 Optimization problems in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
34B15 Nonlinear boundary value problems for ordinary differential equations
74S30 Other numerical methods in solid mechanics (MSC2010)
35S15 Boundary value problems for PDEs with pseudodifferential operators
37-XX Dynamical systems and ergodic theory

Citations:

Zbl 0514.00014