Geodesic
On the behaviour at infinity of solutions to nonlocal parabolic type problems
The Bulletin of Irkutsk State University. Series Mathematics, Tome 30 (2019), pp. 99-113

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The paper deals with possible behaviour at infinity of solutions to the Cauchy problem for a parabolic type equation whose elliptic part is the generator of a Markov jump process , i.e. a nonlocal diffusion operator. The analysis of the behaviour of the solutions at infinity is based on the results on the asymptotics of the fundamental solutions of nonlocal parabolic problems. It is shown that such fundamental solutions might have different asymptotics and decay rates in the regions of moderate, large and super-large deviations. The asymptotic formulae for the said fundamental solutions are then used for describing classes of unbounded functions in which the studied Cauchy problem is well-posed. We also consider the question of uniqueness of a solution in these functional classes.
Keywords: nonlocal operators, fundamental solution, Markov jump process with independent increments.
Mots-clés : parabolic equations 
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     author = {E. A. Zhizhina and A. L. Piatnitski},
     title = {On the behaviour at infinity of solutions to nonlocal parabolic type problems},
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E. A. Zhizhina; A. L. Piatnitski. On the behaviour at infinity of solutions to nonlocal parabolic type problems. The Bulletin of Irkutsk State University. Series Mathematics, Tome 30 (2019), pp. 99-113. http://geodesic.mathdoc.fr/item/IIGUM_2019_30_a7/