This work concerns a nonlinear diffusionแabsorption 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
โฆ LIBER โฆ
Extinction in Finite Time of Solutions to Nonlinear Absorption-Diffusion Equations
โ Scribed by A.V. Lair; M.E. Oxley
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 342 KB
- Volume
- 182
- Category
- Article
- ISSN
- 0022-247X
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This paper studies the Cauchy problem of the 3D NavierโStokes equations with nonlinear damping termโ|โ__u__โ|โ^__ฮฒ__โ1^__u__ (__ฮฒ__โโฅโ1). For __ฮฒ__โโฅโ3, we derive a decay rate of the __L__^2^โnorm of the solutions. Then, the large time behavior is given by comparing the equation with the classic 3D