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Optimal global second-order regularity and improved integrability for parabolic equations with variable growth

Advances in Nonlinear Analysis
We consider the homogeneous Dirichlet problem for the parabolic equation ut−div(∣∇u∣p(x,t)−2∇u)=f(x,t)+F(x,t,u,∇u){u}_{t}-{\rm{div}}({| \nabla u| }^{p\left(x,t)-2}\nabla u)=f\left(x,t)+F\left(x,t,u,\nabla u) in the cylinder QT≔Ω×(0,T){Q}_{T}:= \Omega ...
Arora Rakesh, Shmarev Sergey
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Energy solutions of the Cauchy-Dirichlet problem for fractional nonlinear diffusion equations

2020 MSC: Primary: 35K67 Secondary: 35B40.The present paper is concerned with the Cauchy-Dirichlet problem for fractional (and non-fractional) nonlinear diffusion equations posed in bounded domains.
Akagi, Goro, Salin, Florian
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A critical non-homogeneous heat equation with weighted source

European Journal of Applied Mathematics
Some qualitative properties of radially symmetric solutions to the non-homogeneous heat equation with critical density and weighted source \begin{align*} |x|^{-2}\partial _tu=\Delta u+|x|^{\sigma }u^p, \quad (x,t)\in {\mathbb {R}}^N\times (0,T), \end ...
Razvan Gabriel Iagar, Ariel Sánchez
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Molecular Resources from Transcriptomes in the Brassicaceae Family. [PDF]