We study a class of problems in forced phase transitions in one-dimensional, shape-memory solids. The problems incorporate a prescribed body force B which delivers live loading and a non- convex stored energy function of the strain W. The continuity and differentiability requirements over W and B are standard. Assuming that B is concave and under mild growth conditions on W and B, we obtained existence of minimizers for the functional in the problems posed. Then we showed that the minimizers satisfy the Euler-Lagrange equations of equilibrium almost everywhere. Это и многое другое вы найдете в книге Minimizers for a One-Dimensional Elasticity Problem (Maria Mercedes Franco)
Minimizers for a One-Dimensional Elasticity Problem Maria Mercedes Franco (книга)
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