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Zbl 1183.49015
Kruž{\'\i}k, Martin; Zimmer, Johannes
Evolutionary problems in non-reflexive spaces. (English)
[J] ESAIM, Control Optim. Calc. Var. 16, No. 1, 1-22 (2010). ISSN 1292-8119; ISSN 1262-3377/e

Summary: Rate-independent problems are considered, where the stored energy density is a function of the gradient. The stored energy density may not be quasiconvex and is assumed to grow linearly. Moreover, arbitrary behaviour at infinity is allowed. In particular, the stored energy density is not required to coincide at infinity with a positively 1-homogeneous function. The existence of a rate-independent process is shown in the so-called energetic formulation.

MSC 2000:: *49J45 Optimal control problems inv. semicontinuity and convergence
35B05 General behavior of solutions of PDE
74G65 Energy minimization
49S05 Variational principles of physics
49J20 Optimal control problems with PDE (existence)

Keywords: concentrations; energetic solution; energies with linear growth; oscillations; relaxation

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