Regularity, uniqueness and qualitative behaviour of degenerate parabolic equations of fourth order

Cel

In recent years degenerate parabolic equations of fourth order became important for modelling diffusion processes in Physics and Material Sciences. For example, the spreading of viscous droplets on plain surfaces, the phase separation of binary mixtures and the formation of dislocation patterns during plastic deformation are described by equations the archetypus of which is
Ut + div(|u|n (triangle, triangle) u) = 0.
In one space dimension, Bertsch et al. (BBP, '94) got results concerning regularity, non-uniqueness and qualitative behaviour of solutions. In (G. '94), first results concerning existence and non-negativity in higher space dimensions could be obtained. The objectifives of the project are as follows:
? Optimal results about positivity and evolution of the solution's support in higher space dimensions
? L (infinity)- and C (alpha)- estimates in higher space dimensions ? Formulation of conditions at the free boundary which guarantee uniqueness of solutions
(BBP, '94) E.Beretta M.Bertsch R.DalPasso: Non-negative Solutions of a Fourth Order Non-linear Degenerate Parabolic Equation, to appear in Arch. Rat. Mech. Anal.
(G. '94) G.Grun: Degenerate Parabolic Equations of Fourth Order and a Plasticity Model unith Non-local Hardening to appear in Zeitschrift fuer Analysis und ihre Anwendungen

Program(-y)

FP4-TMR - Specific research and technological development programme in the field of the training and mobility of researchers, 1994-1998

Temat(-y)

Zaproszenie do składania wniosków

Data not available

System finansowania

RGI - Research grants (individual fellowships)

Koordynator

UNIVERSITÀ DEGLI STUDI DI ROMA TOR VERGATA

Adres

Via della ricerca scientifica
00133 Roma
Włochy

Wkład UE

Brak danych

Uczestnicy (1)

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