Cauchy problem for degenerate and uniformly parabolic equations with nonlocal source. Issue 3 (17th February 2017)

• Record Type: Journal Article
• Authors: Shang, Haifeng; Han, Xuefeng; Li, Xiaohong
• Is Part Of: Applicable analysis. Volume 96:Issue 3(2017)
• Page Start: 441
• Page End: 460
• Publication Date: 2017-02-17
• Subjects: Degenerate and uniformly parabolic equation -- Cauchy problem -- nonlocal source -- critical exponent -- existence and nonexistence of solutions; 35K15 -- 35K55 -- 35B33; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2016.1143463
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : The Cauchy problem of the following equation is considered, where, , , and . We are initially interested in the problem of finding sharp conditions ensuring the local existence of solutions, and give the proof of the local existence of solutions. Then our attention is focus on the global existence and nonexistence of solutions. In particular, a Fujita's type critical exponent is obtained. These extend several classical conditions and results to the problem considered here.