A Parabolic Quasilinear Problem for Linear Growth Functionals
FUENSANTA ANDREU, Vicent Caselles, José M. Mazón · Revista Matemática Iberoamericana · 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.