Browsing by Author "Diaz, J.I."

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    On the controllability in a mathematical model of growth of tumors
    (2000-12) Diaz, J.I.; Tello, J.I.
    We study a model of growth of tumors with a free boundary, delaying the tumor region. We take into account the presence of inhhibitors and its interaction with the nutrients. We study the approximate controllability of the internal distribution of density of cells, that is propotional to concentration of nutrients, injecting inhibitor in a small inner region 0 .
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    Some qualitative properties for the total variational flow
    (2000-12) Andreu, F.; Caselles, Vicent; Diaz, J.I.; Mazon, J.M.
    We prove the existence of a finite extinction time for the solutions of the Dirichiet problem for the total variational flow. For the Neumann problem, we prove that the solutions reach the average of its initial datum in finite time. The asymptotic profile of the solutions of the Dirichlet problem is also studied. It is shown that the profiles are non zero solutions of an eigenvalue type problem which seems to be unexplored in the previous literature. The propagation of the support is analyzed in the radial case showing a behaviour enterely different to the case of the problem associated to the p-Laplacian operator. Finally, the study of the radially symmetric case allows us to point out other qualitative properties which are peculiar of this special class of quasilinear equations.