Asymptotics of Fundamental Solutions of Parabolic Problems
Matematičeskie zametki, Tome 115 (2024) no. 2, pp. 219-229.

Voir la notice de l'article provenant de la source Math-Net.Ru

We present several methods for constructing the asymptotics of the fundamental solution of Fokker–Planck–Kolmogorov-type parabolic equations with a small parameter both for small and finite positive times.
Keywords: asymptotics, fundamental solution, small parameter.
Mots-clés : parabolic equation
@article{MZM_2024_115_2_a5,
     author = {V. G. Danilov},
     title = {Asymptotics of {Fundamental} {Solutions} of {Parabolic} {Problems}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {219--229},
     publisher = {mathdoc},
     volume = {115},
     number = {2},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2024_115_2_a5/}
}
TY  - JOUR
AU  - V. G. Danilov
TI  - Asymptotics of Fundamental Solutions of Parabolic Problems
JO  - Matematičeskie zametki
PY  - 2024
SP  - 219
EP  - 229
VL  - 115
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2024_115_2_a5/
LA  - ru
ID  - MZM_2024_115_2_a5
ER  - 
%0 Journal Article
%A V. G. Danilov
%T Asymptotics of Fundamental Solutions of Parabolic Problems
%J Matematičeskie zametki
%D 2024
%P 219-229
%V 115
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2024_115_2_a5/
%G ru
%F MZM_2024_115_2_a5
V. G. Danilov. Asymptotics of Fundamental Solutions of Parabolic Problems. Matematičeskie zametki, Tome 115 (2024) no. 2, pp. 219-229. http://geodesic.mathdoc.fr/item/MZM_2024_115_2_a5/

[1] V. G. Danilov, S. M. Frolovitchev, “Exact asymptotics of the density of the transition probability for discontinuous Markov processes”, Math. Nachr., 215:1 (2000), 55–90 | 3.0.CO;2-R class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI | MR

[2] V. G. Danilov, “Nonsmooth nonoscillating exponential-type asymptotics for linear parabolic PDE”, SIAM J. Math. Anal., 49:5 (2017), 3550–3572 | DOI | MR

[3] S. A. Molchanov, “Diffuzionnye protsessy i rimanova geometriya”, UMN, 30:1 (181) (1975), 3–59 | MR | Zbl

[4] V. P. Maslov, “Globalnaya eksponentsialnaya asimptotika reshenii tunnelnykh uravnenii i zadachi o bolshikh ukloneniyakh”, Mezhdunarodnaya konferentsiya po analiticheskim metodam v teorii chisel i analize (Moskva, 1981), Tr. MIAN SSSR, 163, 1984, 150–180 | MR | Zbl

[5] V. P. Maslov, G. A. Omel'yanov, Geometric Asymptotics for Nonlinear PDE. I, Transl. Math. Monogr., 202, Amer. Math. Soc., Providence, RI, 2001 | MR

[6] V. P. Maslov, V. E. Nazaikinskii, “Tunnelnyi kanonicheskii operator v termodinamike”, Funkts. analiz i ego pril., 40:3 (2006), 12–29 | DOI | MR | Zbl

[7] V. G. Danilov, “A representation of the delta function via creation operators and Gaussian exponentials, and multiplicative fundamental solution asymptotics for some parabolic pseudodifferential equations”, Russian J. Math. Phys., 3:1 (1995), 25–40 | MR

[8] A. M. Ilin, Soglasovanie asimptoticheskikh razlozhenii reshenii kraevykh zadach, Nauka, M., 1989 | MR

[9] V. G. Danilov, D. Mitrovic, “Weak asymptotics of shock wave formation process”, Nonlinear Anal., 61:4 (2005), 613–635 | DOI | MR

[10] P. Cannarsa, H. M. Soner, “On the singularities of the viscosity solutions to Hamilton–Jacobi–Bellman equations”, Indiana Univ. Math. J., 36:3 (1987), 501–524 | DOI | MR

[11] M. G. Crandall, P. L. Lions, “Viscosity solutions of Hamilton–Jacobi equations”, Trans. Amer. Math. Soc., 277:1 (1983), 1–42 | DOI | MR

[12] S. Yu. Dobrokhotov, V. E. Nazaikinskii, A. I. Shafarevich, “Novye integralnye predstavleniya kanonicheskogo operatora Maslova v osobykh kartakh”, Izv. RAN. Ser. matem., 81:2 (2017), 53–96 | DOI | MR