ON THE CONTINUATION OF SOLUTIONS OF NON-AUTONOMOUS SEMILINEAR PARABOLIC PROBLEMS

Author(s)

Carvalho, Alexandre N. ^[1] ; Cholewa, Jan W. ^[2] ; Nascimento, Marcelo J. D. ^[3]

Affiliation

^[1] Univ Sao Paulo, Inst Ciencias Matemat & Comp, Dept Matemat, BR-13560970 Sao Paulo - Brazil

^[2] Silesian Univ, Inst Math, PL-40007 Katowice - Poland

^[3] Univ Fed Sao Carlos, Dept Matemat, BR-13565905 Sao Paulo - Brazil

• Document type: Journal article
• Source: PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY; v. 59, n. 1, p. 17-55, FEB 2016.
• Web of Science Citations: 0

Abstract

We study non-autonomous parabolic equations with critical exponents in a scale of Banach spaces E-sigma, sigma is an element of {[}0,1 + mu). We consider a suitable E1+epsilon-solution and describe continuation properties of the solution. This concerns both a situation when the solution can be continued as an E1+epsilon-solution and a situation when the E1+epsilon-norm of the solution blows up, in which case a piecewise E1+epsilon-solution is constructed. (AU)

• FAPESP's process: 11/51704-2 - Jan Wladyslaw Cholewa | University of Silesia - Polônia
• Grantee: Alexandre Nolasco de Carvalho
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• FAPESP's process: 11/04166-5 - Continuity of attractors to parabolic problems
• Grantee: Marcelo José Dias Nascimento
• Support Opportunities: Regular Research Grants