Geodesic
Solution blowup for systems of shallow-water equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 177 (2013) no. 2, pp. 264-275 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We consider initial-boundary value problems for systems of shallow-water equations. Using the test-function method proposed by Pokhozhaev and Mitidieri, we study the effects of the boundary values and initial conditions on the occurrence, duration, and rate of blowup of the solutions of these problems. Under natural boundary conditions, we prove the existence of blowup in one- and two-dimensional problems in bounded and unbounded regions with dissipation and dispersion.
Keywords: initial-boundary value problem, finite-time blowup, shallow water approximation. 
@article{TMF_2013_177_2_a4,
     author = {M. O. Korpusov and E. V. Yushkov},
     title = {Solution blowup for systems of shallow-water equations},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {264--275},
     year = {2013},
     volume = {177},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2013_177_2_a4/}
}
TY  - JOUR
AU  - M. O. Korpusov
AU  - E. V. Yushkov
TI  - Solution blowup for systems of shallow-water equations
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2013
SP  - 264
EP  - 275
VL  - 177
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_2013_177_2_a4/
LA  - ru
ID  - TMF_2013_177_2_a4
ER  - 
%0 Journal Article
%A M. O. Korpusov
%A E. V. Yushkov
%T Solution blowup for systems of shallow-water equations
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2013
%P 264-275
%V 177
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_2013_177_2_a4/
%G ru
%F TMF_2013_177_2_a4
M. O. Korpusov; E. V. Yushkov. Solution blowup for systems of shallow-water equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 177 (2013) no. 2, pp. 264-275. http://geodesic.mathdoc.fr/item/TMF_2013_177_2_a4/

[1] A. Constantin, J. Escher, Acta Math., 181:2 (1998), 229–243 | DOI | MR | Zbl

[2] Y. Zhou, Nonlinear Anal., 57:1 (2004), 137–152 | DOI | MR | Zbl

[3] O. V. Bulatov, T. G. Elizarova, Zh. vychisl. matem. i matem. fiz., 51:1 (2011), 170–184 | DOI | MR | Zbl

[4] B. L. Rozhdestvenskii, N. N. Yanenko, Sistemy kvazilineinykh uravnenii i ikh prilozheniya k gazovoi dinamike, Nauka, M., 1968 | MR | Zbl

[5] L. D. Landau, E. M. Lifshits, Gidrodinamika, Nauka, M., 1986 | MR | Zbl

[6] S. Yu. Dobrokhotov, S. B. Medvedev, D. S. Minenkov, Matem. zametki, 93:5 (2013), 716–727 | DOI | DOI | MR | Zbl

[7] S. I. Pokhozhaev, Matem. sb., 202:6 (2011), 111–132 | DOI | DOI | MR | Zbl

[8] S. I. Pokhozhaev, Matem. zametki, 89:3 (2011), 393–409 | DOI | DOI | MR | Zbl

[9] S. I. Pokhozhaev, Uravneniya v chastnykh proizvodnykh, SMFN, 39, RUDN, M., 2011, 141–150 | DOI | MR

[10] E. Mitidieri, S. I. Pokhozhaev, Tr. MIAN, 234 (2001), 3–383 | MR | Zbl

[11] V. A. Galaktionov, E. Mitidieri, S. I. Pohozhaev, Nonlinear Anal., 70:8 (1009), 2930–2952 | DOI | MR

[12] A. N. Kolmogorov, S. V. Fomin, Elementy teorii funktsii i funktsionalnogo analiza, Fizmatlit, M., 2006 | MR

[13] C. I. Pokhozhaev, Differents. uravneniya, 47:4 (2011), 493–498 | MR | Zbl

[14] E. V. Yushkov, TMF, 173:2 (2012), 197–206 | DOI | DOI | MR | Zbl

[15] S. Yu. Dobrokhotov, A. I. Shafarevich, Mekhanika zhidkosti i gaza, 31:4 (1996), 38–42 | MR | Zbl

[16] E. V. Yushkov, Differents. uravneniya, 48:9 (2012), 1234–1239 | Zbl

[17] S. Lai, Y. Wu, J. Differ. Equ., 249:3 (2010), 693–706 | DOI | MR | Zbl

[18] M. O. Korpusov, TMF, 174:3 (2013), 355–363 | DOI | DOI | MR | Zbl