Geodesic
Long-time behaviour of two-phase solutions to a class of forward-backward parabolic equations
Flavia Smarazzo1
1Università di Roma "La Sapienza", Italy
Interfaces and free boundaries, Tome 12 (2010) no. 3, pp. 369-408

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DOI

We consider two-phase solutions to the Neumann initial-boundary value problem for the parabolic equation ut=[φ(u)]xx, where φ is a nonmonotone cubic-like function. First, we prove global existence for a restricted class of initial data _u_0, showing that two-phase solutions can be obtained as limiting points of the family of solutions to the Neumann initial-boundary value problem for the regularized equation _ut_ε = [φ(_u_ε)]xx + ε_utxx_ε (ε 0). Then, assuming global existence, we study the long-time behaviour of two-phase solutions for any initial datum _u_0.
DOI : 10.4171/ifb/239
Classification : 35-XX, 28-XX, 00-XX
Mots-clés : Forward-backward equations; two-phase solutions; pseudoparabolic regularization; longtime behaviour of solutions; steady states.

Flavia Smarazzo  1

1 Università di Roma "La Sapienza", Italy 
Flavia Smarazzo. Long-time behaviour of two-phase solutions to a class of forward-backward parabolic equations. Interfaces and free boundaries, Tome 12 (2010) no. 3, pp. 369-408. doi: 10.4171/ifb/239
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     title = {Long-time behaviour of two-phase solutions to a class of forward-backward parabolic equations},
     journal = {Interfaces and free boundaries},
     pages = {369--408},
     year = {2010},
     volume = {12},
     number = {3},
     doi = {10.4171/ifb/239},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/239/}
}
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