Blowup solutions of the nonlinear Thomas equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 201 (2019) no. 1, pp. 54-64 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We study boundary value problems on an interval and on the half-line for the well-known Thomas equation $u_{xt}+\alpha u_x+\beta u_t+u_xu_t=0$, which is a model equation describing processes in chemical kinetics with ion exchange during sorption in a reagent stream. For this equation, we obtain sufficient conditions for its solution blowup in a finite time.
Keywords: Sobolev-type nonlinear equation, blowup, local solvability, nonlinear capacity, blowup time estimate.
@article{TMF_2019_201_1_a3,
     author = {M. O. Korpusov},
     title = {Blowup solutions of the~nonlinear {Thomas} equation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {54--64},
     year = {2019},
     volume = {201},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2019_201_1_a3/}
}
TY  - JOUR
AU  - M. O. Korpusov
TI  - Blowup solutions of the nonlinear Thomas equation
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2019
SP  - 54
EP  - 64
VL  - 201
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_2019_201_1_a3/
LA  - ru
ID  - TMF_2019_201_1_a3
ER  - 
%0 Journal Article
%A M. O. Korpusov
%T Blowup solutions of the nonlinear Thomas equation
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2019
%P 54-64
%V 201
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_2019_201_1_a3/
%G ru
%F TMF_2019_201_1_a3
M. O. Korpusov. Blowup solutions of the nonlinear Thomas equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 201 (2019) no. 1, pp. 54-64. http://geodesic.mathdoc.fr/item/TMF_2019_201_1_a3/

[1] H. C. Thomas, “Heterogeneous ion exchange in a flowing system”, J. Am. Chem. Soc., 66:10 (1944), 1664–1666 | DOI

[2] R. R. Rosales, “Exact solutions of some nonlinear evolution equations”, Stud. Appl. Math., 59:2 (1978), 117–151 | DOI | MR

[3] A. R. Chowdhury, S. Paul, “Laxpair, Lie–Backlund symmetry and hereditary operator for the Thompson equation”, Phys. Scr., 30:1 (1984), 9 | DOI | MR

[4] W. T. Wong, P. C. W. Fung, “Prolongation structure for the Thompson equation”, Nuovo Cimento B, 99:2 (1987), 163–170 | DOI | MR

[5] S. Y. Sakovich, “On the Thomas equation”, J. Phys. A: Math. Gen., 21:23 (1988), L1123–L1126 | DOI | MR

[6] G. M. Wei, Y. T. Gao, H. Zhang, “On the Thomas equation for the ion-exchange operations”, Czech. J. Phys., 52:6 (2002), 749–751 | DOI

[7] S. I. Pokhozhaev, E. Mitidieri, “Apriornye otsenki i otsutstvie reshenii nelineinykh uravnenii i neravenstv v chastnykh proizvodnykh”, Tr. MIAN, 234 (2001), 3–383 | MR | Zbl

[8] V. A. Ditkin, A. P. Prudnikov, Spravochnik po operatsionnomu ischisleniyu, Vysshaya shkola, M., 1965 | Zbl

[9] F. Trikomi, Lektsii po uravneniyam v chastnykh proizvodnykh, IL, M., 1957 | MR | Zbl

[10] G. N. Vatson, Teoriya besselevykh funktsii, IL, M., 1949 | MR | Zbl