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.
On the continuity of the solution of the singular equation (β(u))t = Δu
✍ Scribed by Luca Esposito; Giuseppe Mingione; Bianca Stroffolini
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 107 KB
- Volume
- 36
- Category
- Article
- ISSN
- 0362-546X
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
The PDE ∇u = uV can be treated as its ODE equivalent u = a u if the vector field V satisfies the integrability condition curl V = 0. In this case there exist solutions v of the equation ∇v = V and solutions of the original equation have the form u = ce v (c ∈ ). However, in devising meaningful solut
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
The equation x t y c t x t y is considered in the critical case. For it, the ȧsymptotic behavior of dominant and subdominant solutions is studied. A generalization is made and connections with known results are discussed.