Geodesic
Two-phase entropy solutions of forward–backward parabolic problems with unstable phase
Andrea Terracina1
1Università di Roma La Sapienza, Italy
Interfaces and free boundaries, Tome 17 (2015) no. 3, pp. 289-315

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DOI

In this paper we study a two-phase problem for a forward–backward parabolic equation with diffusion function of cubic type. Existence and uniqueness for these kind of problems were obtained in literature in the case in which the phases are both stable. Here we consider the situation in which the unstable phase is taken in account, obtaining not trivial solutions of the problem. It is interesting to note that such solutions are given by solving generalized Abel’s equations.
DOI : 10.4171/ifb/343
Classification : 35-XX
Mots-clés : Two-phase solutions, phase transition, forward–backward equations, ill-posed problems

Andrea Terracina  1

1 Università di Roma La Sapienza, Italy 
Andrea Terracina. Two-phase entropy solutions of forward–backward parabolic problems with unstable phase. Interfaces and free boundaries, Tome 17 (2015) no. 3, pp. 289-315. doi: 10.4171/ifb/343
@article{10_4171_ifb_343,
     author = {Andrea Terracina},
     title = {Two-phase entropy solutions of forward{\textendash}backward parabolic problems with unstable phase},
     journal = {Interfaces and free boundaries},
     pages = {289--315},
     year = {2015},
     volume = {17},
     number = {3},
     doi = {10.4171/ifb/343},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/343/}
}
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