On the continuation of solutions of non-autonomous semilinear parabolic problems. Issue 1 (13th July 2015)

• Record Type: Journal Article
• Authors: Carvalho, Alexandre N.; Cholewa, Jan W.; Nascimento, Marcelo J. D.
• Is Part Of: Proceedings of the Edinburgh Mathematical Society. Volume 59:Issue 1(2016)
• Page Start: 17
• Page End: 55
• Publication Date: 2015-07-13
• Subjects: abstract parabolic equations, -- continuation of solutions, -- critical exponents; Primary 35K90, -- 35B60, -- 35B33; Mathematics -- Periodicals; 510
• DOI: 10.1017/S001309151400039X
• Languages: English
• ISSNs: 0013-0915

Abstract

Abstract: We study non-autonomous parabolic equations with critical exponents in a scale of Banach spaces Eσ, σ ∈ [0, 1 + μ). We consider a suitable E1+ε -solution and describe continuation properties of the solution. This concerns both a situation when the solution can be continued as an E1+ε -solution and a situation when the E1+ε -norm of the solution blows up, in which case a piecewise E1+ε -solution is constructed.