Global existence of solutions of a semilinear heat equation with nonlinear memory condition. Issue 16 (9th December 2020)

• Record Type: Journal Article
• Authors: Gladkov, Alexander; Guedda, Mohammed
• Is Part Of: Applicable analysis. Volume 99:Issue 16(2020)
• Page Start: 2823
• Page End: 2832
• Publication Date: 2020-12-09
• Subjects: Alexander Pankov; Semilinear parabolic equation -- memory boundary condition -- finite time blow-up; 35K20 -- 35K58 -- 35K61; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2019.1584291
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : We consider a semilinear parabolic equation with flux at the boundary governed by a nonlinear memory. We give some conditions for this problem which guarantee global existence of solutions as well as blow-up in finite time of all nontrivial solutions. The results depend on the behavior of variable coefficients as t → ∞ .