The second critical exponent for a semilinear nonlocal parabolic equation

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:418

Article

Yang, Chunxiao¹  Ji, Feiyu¹  Zhou, Shuangshuang² 

[1] Xian Univ Architecture & Technol, Sch Sci, Xian 710055, Peoples R China

[2] Hunan City Univ, Sch Math & Computat Sci, Yiyang 413000, Peoples R China

关键词: Nonlocal source;    The second critical exponent;    Blow-up;    Global;   

DOI  :  10.1016/j.jmaa.2014.03.095

来源: Elsevier

【 摘 要 】

This article considers the Cauchy problem for a semilinear nonlocal parabolic equation ut = Delta u + (f(R)n, K(y)u(q)(y,t)dy)p-(1/q) u(r+1) in Er x (0,T), where p, q >= 1, gamma >= 0 and p + gamma > 1. We study the second critical exponent, i.e. describing the critical smallness of initial data required by global solutions (non-global solutions) via the decay rates of the initial data at spatial infinity. Differently from other parabolic equations, the second critical exponent is related to n in this problem when K is not an element of L-1 (R-n). (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

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