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Non-Autonomous Maximal Regularity in Hilbert Spaces

, 2016
We consider non-autonomous evolutionary problems of the form $u'(t)+A(t)u(t)=f(t)$, $u(0)=u_0,$ on $L^2([0,T];H)$, where $H$ is a Hilbert space.
Dier, Dominik, Zacher, Rico
core +1 more source

Non-Autonomous Maximal Regularity for Forms of Bounded Variation [PDF]

, 2014
We consider a non-autonomous evolutionary problem \[ u' (t)+\mathcal A (t)u(t)=f(t), \quad u(0)=u_0, \] where $V, H$ are Hilbert spaces such that $V$ is continuously and densely embedded in $H$ and the operator $\mathcal A (t)\colon V\to V^\prime$ is ...
Dier, Dominik
core

Existence of global solutions to reaction-diffusion systems with nonhomogeneous boundary conditions via a Lyapunov functional

Electronic Journal of Differential Equations, 2002
Most publications on reaction-diffusion systems of $m$ components ($mgeq 2$) impose $m$ inequalities to the reaction terms, to prove existence of global solutions (see Martin and Pierre [10 ] and Hollis [4]).
Said Kouachi
doaj

Note on quantitative homogenization results for parabolic systems in R d. [PDF]