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arXiv · 2512.00495

Parabolic problems with slightly superlinear convection terms

Fessel Achhoud
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Abstract

In this paper we deal with a non-linear parabolic problem which involving a convection term with super--linear growth, whose model is \[ \frac{\partial u}{\partial t}-\div(\mathcal{M}(x,t)\nabla u)= -\div(u\log (e+|u|)E(x,t))+f(x,t), \] where $\mathcal{M}$ is a bounded measurable matrix, the vector field $E$ and the function $f$ belong to suitable Lebesgue spaces. We prove the existence of a unique bounded and unbounded weak solution.

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Fessel Achhoud. 2025-11-29. Parabolic problems with slightly superlinear convection terms. https://arxiv.org/abs/2512.00495

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