Geodesic
On the structure of layers for singularly perturbed equations in the case of unbounded energy
ESAIM: Control, Optimisation and Calculus of Variations, Tome 8 (2002), pp. 941-963

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Zbl

We consider singular perturbation variational problems depending on a small parameter ε. The right hand side is such that the energy does not remain bounded as ε→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 ε>0 are elliptic. In the parabolic and hyperbolic cases, the propagation of singularities appear as an integral property after integrating across the layers.

DOI : 10.1051/cocv:2002043
Classification : 35A35, 35B25, 35B40
Keywords: singular perturbations, unbounded energy, propagation of singularities 
Sanchez-Palencia, E. On the structure of layers for singularly perturbed equations in the case of unbounded energy. ESAIM: Control, Optimisation and Calculus of Variations, Tome 8 (2002), pp. 941-963. doi: 10.1051/cocv:2002043
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     title = {On the structure of layers for singularly perturbed equations in the case of unbounded energy},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {941--963},
     year = {2002},
     publisher = {EDP-Sciences},
     volume = {8},
     doi = {10.1051/cocv:2002043},
     zbl = {1070.35005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv:2002043/}
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