Volume 22, Issue 3
Source Type Solutions of a Fourth Order Degenerate Parabolic Equation

Changchun Liu , Songzhe Lian & Zhao Wang

J. Part. Diff. Eq., 22 (2009), pp. 205-217.

Published online: 2009-08

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  • Abstract

In this paper, we study a generalized thin film equation which is relevant to capillary driven flows of thin films of power-law fluids. We prove that the generalized thin film equation in dimension d ≥ 2 has a unique C^1 source type radial self-similar nonnegative solution if 0 < n < 2p-1 and has no solution of this type if n ≥ 2p-1.

  • Keywords

Source type solutions degenerate parabolic equation existence

  • AMS Subject Headings

35K30 35K55 76A20

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COPYRIGHT: © Global Science Press

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@Article{JPDE-22-205, author = {}, title = {Source Type Solutions of a Fourth Order Degenerate Parabolic Equation}, journal = {Journal of Partial Differential Equations}, year = {2009}, volume = {22}, number = {3}, pages = {205--217}, abstract = {

In this paper, we study a generalized thin film equation which is relevant to capillary driven flows of thin films of power-law fluids. We prove that the generalized thin film equation in dimension d ≥ 2 has a unique C^1 source type radial self-similar nonnegative solution if 0 < n < 2p-1 and has no solution of this type if n ≥ 2p-1.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v22.n3.2}, url = {http://global-sci.org/intro/article_detail/jpde/5254.html} }
TY - JOUR T1 - Source Type Solutions of a Fourth Order Degenerate Parabolic Equation JO - Journal of Partial Differential Equations VL - 3 SP - 205 EP - 217 PY - 2009 DA - 2009/08 SN - 22 DO - http://doi.org/10.4208/jpde.v22.n3.2 UR - https://global-sci.org/intro/article_detail/jpde/5254.html KW - Source type solutions KW - degenerate parabolic equation KW - existence AB -

In this paper, we study a generalized thin film equation which is relevant to capillary driven flows of thin films of power-law fluids. We prove that the generalized thin film equation in dimension d ≥ 2 has a unique C^1 source type radial self-similar nonnegative solution if 0 < n < 2p-1 and has no solution of this type if n ≥ 2p-1.

Changchun Liu , Songzhe Lian & Zhao Wang . (2019). Source Type Solutions of a Fourth Order Degenerate Parabolic Equation. Journal of Partial Differential Equations. 22 (3). 205-217. doi:10.4208/jpde.v22.n3.2
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