### On the structure of layers for singularly perturbed equations in the case of unbounded energy

E. Sanchez-Palencia (2002)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider singular perturbation variational problems depending on a small parameter $\epsilon $. The right hand side is such that the energy does not remain bounded as $\epsilon \to 0$. The asymptotic behavior involves internal layers where most of the energy concentrates. Three examples are addressed, with limits elliptic, parabolic and hyperbolic respectively, whereas the problems with $\epsilon \>0$ are elliptic. In the parabolic and hyperbolic cases, the propagation of singularities appear as an integral property after...