Explicit estimates for the continuous dependence in L ([0, T]; L 1 (R d )) of solutions of the equation l v={ } (8(v))+2(.(v)) (in (0, )\_R d with initial condition v(0, } )=h) with respect to the nonlinear continuously differential functions 8 and . are established.
The Number of Peaks of Nonnegative Solutions to Some Nonlinear Degenerate Parabolic Equations
β Scribed by Shigeru Sakaguchi
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 260 KB
- Volume
- 203
- Category
- Article
- ISSN
- 0022-247X
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β¦ Synopsis
We consider the Cauchy problems for some nonlinear degenerate parabolic equations in β«ήβ¬ N for nonzero bounded nonnegative initial data having compact support, and show that the set of peaks of the nonnegative solution consists of one point after a finite time.
π SIMILAR VOLUMES
This work concerns a nonlinear diffusionαabsorption equation with nonlinear boundary flux. The main topic of interest is the problem of finite time extinction, i.e., the solutions vanish after a finite time. The sufficient and necessary conditions for occurrence of extinction are established. It is
## Abstract This paper deals with the initial and boundary value problem for a singular nonlinear parabolic equation. The existence of solutions is established by parabolic regularization. Some properties of solutions, for instance localization and large time behaviour are also discussed. Copyright