Geodesic
Initial boundary value problem for a nonlocal in time parabolic equation
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 1311-1319.

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

This paper deals with a quasi-linear parabolic partial differential equation that includes a nonlocal in time term. This term contains the integral of the solution over the entire time interval, where the problem is considered. The weak solvability of the initial boundary value problem for this equation is proven.
Keywords: initial boundary value problem, solvability.
Mots-clés : nonlocal in time parabolic equation 
@article{SEMR_2018_15_a105,
     author = {V. N. Starovoitov},
     title = {Initial boundary value problem for a nonlocal in time parabolic equation},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1311--1319},
     publisher = {mathdoc},
     volume = {15},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2018_15_a105/}
}
TY  - JOUR
AU  - V. N. Starovoitov
TI  - Initial boundary value problem for a nonlocal in time parabolic equation
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2018
SP  - 1311
EP  - 1319
VL  - 15
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2018_15_a105/
LA  - en
ID  - SEMR_2018_15_a105
ER  - 
%0 Journal Article
%A V. N. Starovoitov
%T Initial boundary value problem for a nonlocal in time parabolic equation
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2018
%P 1311-1319
%V 15
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2018_15_a105/
%G en
%F SEMR_2018_15_a105
V. N. Starovoitov. Initial boundary value problem for a nonlocal in time parabolic equation. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 1311-1319. http://geodesic.mathdoc.fr/item/SEMR_2018_15_a105/

[1] V.N. Starovoitov, B.N. Starovoitova, “Modeling the dynamics of polymer chains in water solution. Application to sensor design”, Journal of Physics: Conference series, 894 (2017), 012088 | DOI

[2] C.V. Pao, “Reaction diffusion equations with nonlocal boundary and nonlocal initial conditions”, Journal of Mathematical Analysis and Applications, 195:3 (1995), 702–718 | DOI | MR | Zbl

[3] V.V. Shelukhin, “A problem with time-averaged data for nonlinear parabolic equations”, Siberian Mathematical Journal, 32:2 (1991), 309–320 | DOI | MR | Zbl

[4] V.V. Shelukhin, “A variational principle for linear evolution problems nonlocal in time”, Siberian Mathematical Journal, 34:2 (1993), 369–384 | DOI | MR | Zbl

[5] A. Sh. Lyubanova, “On nonlocal problems for systems of parabolic equations”, J. Math. Anal. Appl., 421:2 (2015), 1767–1778 | DOI | MR | Zbl

[6] I. Ekeland, R. Témam, Convex analysis and variational inequalities, North-Holland, Amsterdam, 1976 | MR

[7] H. Gajewski, K. Gröger, K. Zacharias, “Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen”, Mathematische Lehrbücher und Monographien, v. II, Mathematische Monographien, 38, Abteilung, Akademie-Verlag, Berlin, 1974 | MR | Zbl