We prove the Holder continuity of the interface of a solution of a porous medium equation with bounded measurable coefficients. We also describe the asymptotic behaviour as time goes to infinity.
Regularity of the Interfaces with Sign Changes of Solutions of the One-Dimensional Porous Medium Equation
β Scribed by Shigeru Sakaguchi
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 331 KB
- Volume
- 178
- Category
- Article
- ISSN
- 0022-0396
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
The blowup of solutions of the Cauchy problem { u t =u xx + |u| p&1 u u(x, 0)=u 0 (x) in R\\_(0, ), in R is studied. Let 4 k be the set of functions on R which change sign k times. It is shown that for p k =1+2Γ(k+1), k=0, 1, 2, ... , any solution with u 0 # 4 k blows up in finite time if 1 p k . T
## Abstract It is wellβestablished that renormalized solutions of the Boltzmann equation enjoy some kind of regularity, or at least compactness, in the velocity variable when the angular collision kernel is nonintegrable. However, obtaining explicit estimates in convenient and natural functional se
## Abstract We consider the porous media equation with absorption for various conditions and prove that the shape of ist interface never becomes strongly upward convex. For this sake we derive an improperly posed estimate for solutions of the porous media equation for the nonβcharacteristic Cauchy