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European Mathematical Society Publishing House
2016-09-19 17:05:43
Revista Matemática Iberoamericana
Rev. Mat. Iberoamericana
RMI
0213-2230
2235-0616
General
10.4171/RMI
http://www.ems-ph.org/doi/10.4171/RMI
subscribers
European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society (from 2012)
18
2002
1
A Parabolic Quasilinear Problem for Linear Growth Functionals
Fuensanta
Andreu
Universitat de Valencia, BURJASSOT (VALENCIA), SPAIN
Vicent
Caselles
Universitat Pompeu-Fabra, BARCELONA, SPAIN
José
Mazón
Universitat de Valencia, BURJASSOT (VALENCIA), SPAIN
Linear growth functionals, nonlinear parabolic equations, accretive operators, nonlinear semigroups
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.
Partial differential equations
Operator theory
General
135
185
10.4171/RMI/314
http://www.ems-ph.org/doi/10.4171/RMI/314