Abstract
We want to analyze both regularizing effect and long, short time decay concerning a class of parabolic equations having first order superlinear terms. The model problem is the following:
where \(\Omega \) is an open bounded subset of \({{\,\mathrm{{{\mathbb {R}}}}\,}}^N\), \(N\ge 2\), \(0<T\le \infty \), \(1<p<N\) and \(q<p\). We assume that A(t, x) is a coercive, bounded and measurable matrix, the growth rate q of the gradient term is superlinear but still subnatural, \(\gamma \) is a positive constant, and the initial datum \(u_0\) is an unbounded function belonging to a well precise Lebesgue space \(L^\sigma (\Omega )\) for \(\sigma =\sigma (q,p,N)\).
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Magliocca, M. Regularizing effect and decay results for a parabolic problem with repulsive superlinear first order terms. RACSAM 115, 77 (2021). https://doi.org/10.1007/s13398-021-01010-w
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DOI: https://doi.org/10.1007/s13398-021-01010-w