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Extinction in Finite Time of Solutions to Nonlinear Absorption-Diffusion Equations

โœ 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 work concerns a nonlinear diffusionแސabsorption 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

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This paper studies the Cauchy problem of the 3D Navierโ€“Stokes equations with nonlinear damping termโ€‰|โ€‰__u__โ€‰|โ€‰^__ฮฒ__โˆ’1^__u__ (__ฮฒ__โ€‰โ‰ฅโ€‰1). For __ฮฒ__โ€‰โ‰ฅโ€‰3, we derive a decay rate of the __L__^2^โ€norm of the solutions. Then, the large time behavior is given by comparing the equation with the classic 3D