Geodesic
Kinetic formulation of forward-backward parabolic equations
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 13 (2016), pp. 930-949

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We have proved that Dirichlet boundary value problem for nonlinear forward-backward parabolic equation has the unique entropy solution. The main difficulty is that initial and final conditions must be formulated in the form of inequalities. We have used here kinetic formulation of the boundary value problem.
Keywords: entropy solution, kinetic solution, forward-backward parabolic equation. 
@article{SEMR_2016_13_a85,
     author = {I. V. Kuznetsov},
     title = {Kinetic formulation of forward-backward parabolic equations},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {930--949},
     publisher = {mathdoc},
     volume = {13},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2016_13_a85/}
}
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I. V. Kuznetsov. Kinetic formulation of forward-backward parabolic equations. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 13 (2016), pp. 930-949. http://geodesic.mathdoc.fr/item/SEMR_2016_13_a85/