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This article is cited in 1 scientific paper (total in 1 paper)
Integro-differential equations and functional analysis
On the behaviour at infinity of solutions to nonlocal parabolic type problems
E. A. Zhizhinaa, A. L. Piatnitskiab a Institute for Information Transmission Problems of Russian Academy of Siences (IITP RAS), Moscow, Russian Federation
b The Arctic University of Norway, Campus Narvik, Norway
Abstract:
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, parabolic equations, fundamental solution, Markov jump process with independent increments.
Received: 30.10.2019
Citation:
E. A. Zhizhina, A. L. Piatnitski, “On the behaviour at infinity of solutions to nonlocal parabolic type problems”, Bulletin of Irkutsk State University. Series Mathematics, 30 (2019), 99–113
Linking options:
https://www.mathnet.ru/eng/iigum398 https://www.mathnet.ru/eng/iigum/v30/p99
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Abstract page: | 124 | Full-text PDF : | 39 | References: | 12 |
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