On the continuation of solutions of non-autonomous semilinear parabolic problems
AN Carvalho, JW Cholewa… - Proceedings of the …, 2016 - cambridge.org
AN Carvalho, JW Cholewa, MJD Nascimento
Proceedings of the Edinburgh Mathematical Society, 2016•cambridge.orgWe 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.
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.
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.
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