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Pré-Publication, Document De Travail Année : 2012

Initial value problems for diffusion equations with singular potential

Résumé

Let $V$ be a nonnegative locally bounded function defined in $Q_\infty:=\BBR^n\times(0,\infty)$. We study under what conditions on $V$ and on a Radon measure $\gm$ in $\mathbb{R}^d$ does it exist a function which satisfies $\partial_t u-\xD u+ Vu=0$ in $Q_\infty$ and $u(.,0)=\xm$. We prove the existence of a subcritical case in which any measure is admissible and a supercritical case where capacitary conditions are needed. We obtain a general representation theorem of positive solutions when $t V(x,t)$ is bounded and we prove the existence of an initial trace in the class of outer regular Borel measures.
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Dates et versions

hal-00736712 , version 1 (28-09-2012)
hal-00736712 , version 2 (02-10-2012)
hal-00736712 , version 3 (12-10-2012)
hal-00736712 , version 4 (24-10-2012)
hal-00736712 , version 5 (15-11-2012)

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Citer

Konstantinos Gkikas, Laurent Veron. Initial value problems for diffusion equations with singular potential. 2012. ⟨hal-00736712v4⟩
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