Existence and non-existence of global solutions for a higher-order semilinear parabolic system

@article{Pang2006ExistenceAN,
  title={Existence and non-existence of global solutions for a higher-order semilinear parabolic system},
  author={P. Pang and Fuqin Sun and M. Wang},
  journal={Indiana University Mathematics Journal},
  year={2006},
  volume={55},
  pages={1113-1134}
}
In this paper, we study the higher-order semilinear parabolic system u t + (-Δ) m u = |v| p , (t, x) ∈ R 1 + × R N , v t + (-Δ) m v = |u| q , (t, x) ∈ R 1 + × R N , u(0, x) = u 0 (x), v(0, x) = v 0 (x), x ∈ R N , where m > 1, p, q > 1 and pq > 1. We prove that if N/2m > max {1+p/pq-1' 1+q/pq-1} then solutions with small initial data exist globally in time. If the exponents p, q meet some additional conditions, we can derive decay estimates ∥u(t)∥ ∞ ≤ C(1+t) -σ' , ∥v(t)∥ ∞ ≤ C(1+t) -σ" , where… Expand
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