A waiting time phenomenon for thin film equations

• Roberta Dal Passo ^[2] ; Lorenzo Giacomelli ^[1] ; Günther Grün ^[3]
  1. [1] Università de Roma La Sapienza

     Università de Roma La Sapienza

     Roma Capitale, Italia

     
  2. [2] Università di Roma "Tor Vergata", Italia
  3. [3] Universität Bonn, Germany

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• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 30, Nº 2, 2001, págs. 437-463
• Idioma: inglés
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• Resumen

  • We prove the occurrence of a waiting time phenomenon for solutions to fourth order degenerate parabolic differential equations which model the evolution of thin films of viscous fluids. In space dimension less or equal to three, we identify a general criterion on the growth of initial data near the free boundary which guarantees that for sufficiently small times the support of strong solutions locally does not increase. It turns out that this condition only depends on the smoothness of the diffusion coefficient in its point of degeneracy. Our approach combines a new version of Stampacchia’s iteration lemma with weighted energy or entropy estimates. On account of numerical experiments, we conjecture that the aforementioned growth criterion is optimal.