Global regularity of solution for general degenerate parabolic equations in 1-D
This paper considers the Cauchy problem for the general degenerate parabolic equations (1.1) with initial data (1.2). In the critical condition meas{u:g(u)=0{=0 we obtain the regular estimateG(u)∈C(1), whereG(u)=∫u0g(s)ds. A new maximum principle is introduced to obtain the estimate and is applied t...
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| Main Authors: | , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
25 May 2002
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| In: |
Journal of differential equations
Year: 1997, Volume: 140, Issue: 2, Pages: 365-377 |
| ISSN: | 1090-2732 |
| DOI: | 10.1006/jdeq.1997.3313 |
| Online Access: | Resolving-System, Volltext: http://dx.doi.org/10.1006/jdeq.1997.3313 Verlag, Volltext: http://www.sciencedirect.com/science/article/pii/S0022039697933131 
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| Author Notes: | W. Jäger and Yunguang Lu |
| Summary: | This paper considers the Cauchy problem for the general degenerate parabolic equations (1.1) with initial data (1.2). In the critical condition meas{u:g(u)=0{=0 we obtain the regular estimateG(u)∈C(1), whereG(u)=∫u0g(s)ds. A new maximum principle is introduced to obtain the estimate and is applied to some special equations such as prous media equation, an infiltration equation to obtain the optimal estimate |(um−1)x|⩽M. Finally an interesting equation related to the Broadwell model (whereg(u) has two zero points) is studied and a uniquely regular solutionu∈C(1)is obtained. Moreover the estimatesux⩽ρ(f(u)−u2)/g(u) andρ⩾infxρ0(x)/(1+4t(infxρ0(x))) are proved for the solution of the Navier-Stokes equations corresponding to the Broadwell model. |
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| Item Description: | Available online 25 May 2002 Gesehen am 30.07.2018 |
| Physical Description: | Online Resource |
| ISSN: | 1090-2732 |
| DOI: | 10.1006/jdeq.1997.3313 |