Lower bounds on waiting times for degenerate parabolic equations and systems | Zendy

Lorenzo Giacomelli | Zendy; Günther Grün | Zendy

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Lower bounds on waiting times for degenerate parabolic equations and systems

Author(s) -

Lorenzo Giacomelli,

Günther Grün

Publication year - 2006

Publication title -

interfaces and free boundaries mathematical analysis computation and applications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.964

H-Index - 39

eISSN - 1463-9971

pISSN - 1463-9963

DOI - 10.4171/ifb/137

Subject(s) - degenerate energy levels , mathematics , parabolic partial differential equation , assertion , scaling , porous medium , class (philosophy) , independent equation , mathematical analysis , partial differential equation , physics , computer science , geometry , porosity , quantum mechanics , geotechnical engineering , artificial intelligence , engineering , programming language

We extend the method in [Dal Passo Giacomelli Gruen, Annali SNS Pisa, 2001] to obtain quantitative estimates of waiting times for free boundary problems associated with degenerate parabolic equations and systems. Our approach is multidimensional, it applies to a large class of equations, including thin-film equations, (doubly) degenerate equations of second and of higher order and also systems of semiconductor equations. For these equations, we obtain lower bounds on waiting times which we expect to be optimal in terms of scaling. This assertion is true for the porous-medium equation which seems to be the only PDE for which two-sided quantitative estimates of the waiting time have been established so far

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