On the continuation of solutions of non-autonomous semilinear parabolic problems. Issue 1 (13th July 2015) - Carvalho, Alexandre N.; Cholewa, Jan W.; Nascimento, Marcelo J. D.
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.