We consider the inequality u t ≥ u -1 2 x • ∇u + λu + h x t u p , for p > 1 λ ∈ , posed in N × + N ≥ 1. We show that, in certain growth conditions, there is an absence of global weak solutions.
A Note on Nonexistence of Global Solutions to ut ≥ Δu − 12x · ∇u + λu + h(x, t)|u|p: Volume 255, Number 2 (2001), pages 714–722
✍ Scribed by Mohammed Guedda
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 25 KB
- Volume
- 263
- Category
- Article
- ISSN
- 0022-247X
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are presented. The proofs are based on the alternative method, a connectedness result, the contraction mapping principle, and a detailed analysis of the bifurcation equation utilizing, e.g., a generalization of the mean value theorem for integrals. We shall obtain results with g bounded or unbounded
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Consider the quasilinear Cauchy problem where a>0, p and q satisfy p 0 and q 1 or p>1 and q=0, and This paper proves that the above equation possesses a unique positive classical solution and then investigates whether or not ##lim t Ä R d u(x, t) dx=0. In particular, it is shown that if a is on th