We prove existence and uniqueness of solutions for the Dirichlet
problem for quasilinear parabolic equations in divergent form for
which the energy functional has linear growth. A typical example of
energy functional we consider is the one given by the nonparametric
area integrand $f(x, \xi) = \sqrt{1 + \Vert \xi \Vert^2}$, which
corresponds with the time-dependent minimal surface equation. We
also study the asymptotic behaviour of the solutions.
Publié le : 2002-03-14
Classification:
Linear growth functionals,
nonlinear parabolic equations,
accretive operators,
nonlinear semigroups,
35K65,
35K55,
47H06,
47H20
@article{1045578696,
author = {Andreu, Fuensanta and Caselles, Vincent and Maz\'on, Jose\'e Mar\'\i a},
title = {A Parabolic Quasilinear Problem for Linear Growth Functionals},
journal = {Rev. Mat. Iberoamericana},
volume = {18},
number = {1},
year = {2002},
pages = { 135-185},
language = {en},
url = {http://dml.mathdoc.fr/item/1045578696}
}
Andreu, Fuensanta; Caselles, Vincent; Mazón, Joseé María. A Parabolic Quasilinear Problem for Linear Growth Functionals. Rev. Mat. Iberoamericana, Tome 18 (2002) no. 1, pp. 135-185. http://gdmltest.u-ga.fr/item/1045578696/