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On the continuation of solutions of non-autonomous semilinear parabolic problems
Published online by Cambridge University Press: 13 July 2015
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.
MSC classification
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- Research Article
- Information
- Proceedings of the Edinburgh Mathematical Society , Volume 59 , Issue 1 , February 2016 , pp. 17 - 55
- Copyright
- Copyright © Edinburgh Mathematical Society 2016
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