A Parabolic quasilinear problem for linear growth functionals
A Parabolic quasilinear problem for linear growth functionals
Citació
- Andreu F, Caselles V, Mazón JM. A Parabolic quasilinear problem for linear growth functionals. Revista Matemática Iberoamericana. 2002 Abr 30;18(1):135-58. DOI: 10.4171/RMI/314
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Descripció
Resum
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,ξ)=√1+∥ξ∥2, which corresponds with the time-dependent minimal surface equation. We also study the asymptotic behaviour of the solutions.