Global, small amplitude solutions to nonlinear evolution equations
β Scribed by S. Klainerman; Gustavo Ponce
- Publisher
- John Wiley and Sons
- Year
- 1983
- Tongue
- English
- Weight
- 318 KB
- Volume
- 36
- Category
- Article
- ISSN
- 0010-3640
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π SIMILAR VOLUMES
The existence and uniqueness are proved for global classical solutions of the spatially periodic Cauchy problem to the following system of parabolic equations s y y β£ y q β£ Ε½ . which was proposed as a substitute for the RayleighαBenard equation and can lead to Lorenz equations.
## Communicated by X. Wang In this work, we prove the existence of global attractor for the nonlinear evolution equation . This improves a previous result of Xie and Zhong in (J. Math. Anal. Appl. 2007; 336:54-69.) concerning the existence of global attractor in H 1 0 (X)ΓH 1 0 (X) for a similar
A criterion for the nonexplosion of solutions to semilinear evolution equations on Banach spaces is proved. The result is obtained by applying a modification of the Bihari type inequality to the case of a weakly singular nonlinear integral inequality.