Global regularity of solution for general degenerate parabolic equations in 1-D - Jäger, Willi; Lu, Yunguang (Journal of differential equations, 2002)
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.
Available online 25 May 2002
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