Please use this identifier to cite or link to this item: https://doi.org/10.1512/iumj.2006.55.2763
Title: Existence and non-existence of global solutions for a higher-order semilinear parabolic system
Authors: Pang, P.Y.H. 
Sun, F.
Wang, M.
Keywords: Decay estimates
Existence and non-existence
Global solutions
Higher-order parabolic system
Issue Date: 2006
Citation: Pang, P.Y.H., Sun, F., Wang, M. (2006). Existence and non-existence of global solutions for a higher-order semilinear parabolic system. Indiana University Mathematics Journal 55 (3) : 1113-1134. ScholarBank@NUS Repository. https://doi.org/10.1512/iumj.2006.55.2763
Abstract: In this paper, we study the higher-order semilinear parabolic system {ut + (-Δ)mu= |v|p, (t,x) ∈ ℝ+ 1 × ℝN, vt + (-Δ)mv = |u|q, (t,x) ∈ ℝ+ 1 × ℝN, u(0,x) = u0(x), v(0,x) = v0(x), x ∈ ℝN, 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 σ′ and σ″ are positive constants. On the other hand, if N/2m < max{1 + p/pq - 1, 1 + q/pq - 1}, then every solution with initial data having positive average value does not exist globally in time. Indiana University Mathematics Journal ©.
Source Title: Indiana University Mathematics Journal
URI: http://scholarbank.nus.edu.sg/handle/10635/103225
ISSN: 00222518
DOI: 10.1512/iumj.2006.55.2763
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