Solutions of a fourth order degenerate parabolic equation with weak initial trace

Roberta Dal Passo; Harald Garcke

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1999)

  • Volume: 28, Issue: 1, page 153-181
  • ISSN: 0391-173X

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Dal Passo, Roberta, and Garcke, Harald. "Solutions of a fourth order degenerate parabolic equation with weak initial trace." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 28.1 (1999): 153-181. <http://eudml.org/doc/84370>.

@article{DalPasso1999,
author = {Dal Passo, Roberta, Garcke, Harald},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {weak initial data; Radon measure; regularizing effect; existence theorem},
language = {eng},
number = {1},
pages = {153-181},
publisher = {Scuola normale superiore},
title = {Solutions of a fourth order degenerate parabolic equation with weak initial trace},
url = {http://eudml.org/doc/84370},
volume = {28},
year = {1999},
}

TY - JOUR
AU - Dal Passo, Roberta
AU - Garcke, Harald
TI - Solutions of a fourth order degenerate parabolic equation with weak initial trace
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1999
PB - Scuola normale superiore
VL - 28
IS - 1
SP - 153
EP - 181
LA - eng
KW - weak initial data; Radon measure; regularizing effect; existence theorem
UR - http://eudml.org/doc/84370
ER -

References

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  1. [BBD] E. Beretta - M. Bertsch - R. Dal Passo, Nonnegative solutions of a fourth order nonlinear degenerate parabolic equation, Arch. Rational Mech. Anal.129 (1995), 175-200. Zbl0827.35065MR1328475
  2. [B1] F. Bernis, Viscous flows, fourth order nonlinear degenerate parabolic equations and singular elliptic problems, In: "Free boundary problems: theory and applications", (J.I. Diaz, M.A. Herrero, A. Linan and J. L. Vazquez Editors) Pitman Research Notes in Mathematics 323, Longman, Harlow, 1995, pp. 40-56. Zbl0839.35102MR1342325
  3. [B2] F. Bernis, Finite speed of propagation and continuity of the interface for thin viscous flows, Adv. Differential Equations1 (1998) 337-368. Zbl0846.35058MR1401398
  4. [B3] F. Bernis, Integral inequalities with applications to nonlinear degenerate parabolic equations, In: "Nonlinear Problems in Applied Mathematics", (Angell, Cook, Kleinman and Olmstad Editors) Volume in honour of Ivar Stakgold, SIAM, Philadelphia (1996) 57-65. Zbl0889.35054
  5. [B4] F. Bernis, Finite speed of propagation for thin viscous flows when 2 &lt; n &lt; 3, C.R. Acad. Sci. Paris, Sér. I Math.322 (1996), 1169-1174. Zbl0853.76018MR1396660
  6. [BF] F. Bernis - A. Friedman, Higher order nonlinear degenerate parabolic equations, J. Differential Equations83 (1990) 179-206. Zbl0702.35143MR1031383
  7. [BPW] F. Bernis - L.A. Peletier - S.M. Williams, Source type solutions of a fourth order nonlinear degenerate parabolic equation, Nonlinear Anal.18 (1992) 217-234. Zbl0778.35056MR1148286
  8. [BDGG] M. Bertsch - R. Dal Passo - H. Garcke - G. Grün, The thin viscous flow equation in higher space dimensions, Adv. Differential Equations3 (1998) 417-440. Zbl0954.35035MR1751951
  9. [BP] A.L. Bertozzi - M. Pugh, The lubrication approximation for thin viscous films: regularity and long time behaviour of weak solutions, Comm. Pure Appl. Math.49 (1996) 85-123. Zbl0863.76017MR1371925
  10. [DGG] R. Dal Passo - H. Garcke - G. Grün, On a fourth order degenerate parabolic equation: global entropy estimates and qualitative behaviour of solutions, SIAM J. Math. Anal.29 (1998) 321-342. Zbl0929.35061MR1616558
  11. [EG] C.M. Elliott - H. Garcke, On the Cahn-Hilliard equation with degenerate mobility, SIAM J. Math. Anal.27 (1996) 404-423. Zbl0856.35071MR1377481
  12. [EvG] L.C. Evans - R.F. Gariepy, "Measure Theory and Fine Properties of Functions", CRC Press, Boca Raton - Ann Arbor - London, 1992. Zbl0804.28001MR1158660
  13. [FB] R. Ferreira - F. Bernis, Source-type solutions to thin-film equations in higher dimensions, European J. Appl. Math.8 (1997) 507-524. Zbl0894.76019MR1479525
  14. [Ga] E. Gagliardo, Ulteriori proprietà di alcune classi difunzioni in più variabili, Ricerche Mat. Napoli8 (1959) 24-51. Zbl0199.44701MR109295
  15. [G] G. Grün, Degenerate parabolic differential equations of fourth order and a plasticity model with nonlocal hardening, Z. Anal. Anwendungen14 (1995) 541-574. Zbl0835.35061MR1362530
  16. [HS] J. Hulshof - A.E. Shiskov, The thin film equation with 2 &lt; n &lt; 3: finite speed of propagation in terms of the L 1-norm, Adv. Differential Equations (to appear). Zbl0953.35072
  17. [Ni] L. Nirenberg, An extended interpolation inequality, Ann. Scuola Norm. Sup. Pisa Cl. Sci.20 (1966) 733-737. Zbl0163.29905MR208360
  18. [YG] J. Yin - W. Gao, Solutions with compact support to the Cauchy problem of an equation modeling the motion of viscous droplets, Z. Angew. Math. Phys.47 (1966) 659-671. Zbl0862.35094MR1420850

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