Open Access
March, 2002 A Parabolic Quasilinear Problem for Linear Growth Functionals
Fuensanta Andreu, Vincent Caselles, Joseé María Mazón
Rev. Mat. Iberoamericana 18(1): 135-185 (March, 2002).


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.


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Fuensanta Andreu. Vincent Caselles. Joseé María Mazón. "A Parabolic Quasilinear Problem for Linear Growth Functionals." Rev. Mat. Iberoamericana 18 (1) 135 - 185, March, 2002.


Published: March, 2002
First available in Project Euclid: 18 February 2003

zbMATH: 1010.35063
MathSciNet: MR1924690

Primary: 35K55 , 35K65 , 47H06 , 47H20

Keywords: Accretive operators , linear growth functionals , nonlinear parabolic equations , nonlinear semigroups

Rights: Copyright © 2002 Departamento de Matemáticas, Universidad Autónoma de Madrid

Vol.18 • No. 1 • March, 2002
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