Geodesic
The Destruction of the Solution of the Nonlocal Equation with Gradient Nonlinearity
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, no. 11 (2012), pp. 43-53 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this paper we continue our consideration of equations with gradient nonlinearities. In this paper, we consider initial-boundary value problem in a bounded domain with smooth boundary for non-local in time equation with gradient nonlinearity and prove the local solvability of the strong generalized sense, in addition, we obtain sufficient conditions for the destruction of a finite time and sufficient conditions for global in time solubility.
Keywords: nonlocal equation with gradient nonlinearity, the destruction of the solutions.
Mots-clés : Sobolev type equations 
@article{VYURU_2012_11_a4,
     author = {M. O. Korpusov},
     title = {The {Destruction} of the {Solution} of the {Nonlocal} {Equation} with {Gradient} {Nonlinearity}},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
     pages = {43--53},
     year = {2012},
     number = {11},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VYURU_2012_11_a4/}
}
TY  - JOUR
AU  - M. O. Korpusov
TI  - The Destruction of the Solution of the Nonlocal Equation with Gradient Nonlinearity
JO  - Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie
PY  - 2012
SP  - 43
EP  - 53
IS  - 11
UR  - http://geodesic.mathdoc.fr/item/VYURU_2012_11_a4/
LA  - ru
ID  - VYURU_2012_11_a4
ER  - 
%0 Journal Article
%A M. O. Korpusov
%T The Destruction of the Solution of the Nonlocal Equation with Gradient Nonlinearity
%J Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie
%D 2012
%P 43-53
%N 11
%U http://geodesic.mathdoc.fr/item/VYURU_2012_11_a4/
%G ru
%F VYURU_2012_11_a4
M. O. Korpusov. The Destruction of the Solution of the Nonlocal Equation with Gradient Nonlinearity. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, no. 11 (2012), pp. 43-53. http://geodesic.mathdoc.fr/item/VYURU_2012_11_a4/

[1] Sviridyuk G. A., “On the General Theory of Operator Semigroups”, Russ. Math. Surv., 49:4 (1994), 45–74 | MR | Zbl

[2] Sviridyuk G. A., “One Problem for the Generalized Boussinesq Filtration Equation”, Russian Mathematics, 1989, no. 2, 55–61

[3] Sviridyuk G. A., “Quasistationary Trajectories of Semilinear Dynamical Equations of Sobolev type”, Russian Acad. Sci. Izv. Math., 42:3 (1994), 601–614 | DOI | MR | Zbl

[4] Sviridyuk G. A., “Phase Spaces of Semilinear Equations of Sobolev Type with Relatively Strongly Sectorial Operator”, Algebra i analiz, 6:5 (1994), 252–272

[5] Korpusov M. O., “Blow-up Solutions of the Equation with Gradient Nonlinearity”, Differential Equations

[6] Bonch-Bruevich V. L., Kalashnikov S. G., Physics of Semiconductors, Nauka, M., 1990, 672 pp.

[7] Bonch-Bruevich V. L., Zvyagin I. P., Mironov A. G., Blast Electric Instability in Semiconductors, Nauka, M., 1972, 417 pp.

[8] Landau L. D., Lifshits E. M., Theoretical Physics, v. 8, Electrodynamics of Continuous Media, Nauka, M., 1992, 664 pp. | MR

[9] Bass F. G., Bochkov V. S., Gurevich Yu. S., Electrons and Phonons in a Limited Semiconductors, Nauka, M., 1984, 288 pp.

[10] Lions Zh.-L., Some Methods for Solving Nonlinear Boundary Value Problems, Mir, M., 1972, 588 pp. | MR

[11] Demidovich V. P., Lectures on the Mathematical Theory of Stability, Nauka, M., 1967, 472 pp. | MR

[12] Samarskiy A. A., Galaktionov V. A., Kurdyumov S. P., Mikhaylov A. P., Regimes with Peaking in Problems for Quasilinear Parabolic Equations, Nauka, M., 1987, 480 pp. | MR

[13] Vatson G. N., The theory of Bessel functions, v. I, Izd-vo Inostr. lit., M., 1949, 800 pp.