Global Existence and Blow-Up of Solutions to a Parabolic Nonlocal Equation Arising in a Theory of Thermal Explosion. (28th June 2022)

• Record Type: Journal Article
• Authors: Ma, Wenyuan; Zhao, Zhixuan; Yan, Baoqiang
• Other Names: Hussain Azhar Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2022(2022)
• Publication Date: 2022-06-28
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2022/4629799
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : Focusing on the physical context of the thermal explosion model, this paper investigates a semilinear parabolic equation u t = Δ u + a ∫ Ω u p d x, x, t ∈ Q T, n · ∇ u + g u u = 0, x, t ∈ S T, u x, 0 = u 0 x, x ∈ Ω with nonlocal sources under nonlinear heat-loss boundary conditions, where a, p > 0 is constant, Q T = Ω × 0, T, S T = ∂ Ω × 0, T, and Ω is a bounded region in R N, N ≥ 1 with a smooth boundary ∂ Ω . First, we prove a comparison principle for some kinds of semilinear parabolic equations under nonlinear boundary conditions; using it, we show a new theorem of subsupersolutions. Secondly, based on the new method of subsupersolutions, the existence of global solutions and blow-up solutions is presented for different values of p . Finally, the blow-up rate for solutions is estimated also.