Geodesic
An investigation of the behavior of $L_2$-norms of the solutions of strongly parabolic systems with dissipation
Izvestiya. Mathematics, Tome 7 (1973) no. 3, pp. 675-689 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

It is established under certain interrelations between the growth of the initial function and the dissipation intensity that an increasing solution becomes with the passage of time a bounded and ultimately decreasing function of the spatial coordinates. The behavior of $L_2$-norms (containing weights depending in a special manner on the time $t$) of the solutions is investigated for this purpose. The results are essentially based on inequalities established in the paper between the norms and quasinorms introduced and which, in our view, are of independent interest. 
@article{IM2_1973_7_3_a11,
     author = {S. D. \`Eidel'man and F. O. Porper},
     title = {An investigation of the behavior of $L_2$-norms of the solutions of strongly parabolic systems with dissipation},
     journal = {Izvestiya. Mathematics},
     pages = {675--689},
     year = {1973},
     volume = {7},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1973_7_3_a11/}
}
TY  - JOUR
AU  - S. D. Èidel'man
AU  - F. O. Porper
TI  - An investigation of the behavior of $L_2$-norms of the solutions of strongly parabolic systems with dissipation
JO  - Izvestiya. Mathematics
PY  - 1973
SP  - 675
EP  - 689
VL  - 7
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/IM2_1973_7_3_a11/
LA  - en
ID  - IM2_1973_7_3_a11
ER  - 
%0 Journal Article
%A S. D. Èidel'man
%A F. O. Porper
%T An investigation of the behavior of $L_2$-norms of the solutions of strongly parabolic systems with dissipation
%J Izvestiya. Mathematics
%D 1973
%P 675-689
%V 7
%N 3
%U http://geodesic.mathdoc.fr/item/IM2_1973_7_3_a11/
%G en
%F IM2_1973_7_3_a11
S. D. Èidel'man; F. O. Porper. An investigation of the behavior of $L_2$-norms of the solutions of strongly parabolic systems with dissipation. Izvestiya. Mathematics, Tome 7 (1973) no. 3, pp. 675-689. http://geodesic.mathdoc.fr/item/IM2_1973_7_3_a11/

[1] Eidelman S. D., Parabolicheskie sistemy, Nauka, M., 1964 | MR

[2] Takasi Kusano, “On the behavior for large $|x|$ of solutions of parabolic equations with unbounded coefficients”, Funkcialaj Ekvacioj, 11 (1968), 169–174 | MR

[3] Takasi Kusano, “Remarks on the behavior of solutions of second order parabolic equations with unbounded coefficients”, Funkcialaj Ekvacioj, 11 (1968), 197–205 | MR

[4] Eidelman S. D., “Integralnyi printsip maksimuma dlya silno parabolicheskikh sistem i nekotorye ego prilozheniya”, Izv. vyssh. uchebn. zavedenii, Matematika, 1959, no. 2(9), 252–258 | MR | Zbl

[5] Fridman A., Uravneniya s chastnymi proizvodnymi parabolicheskogo tipa, Mir, M., 1968

[6] Kostyuchenko A. G., “Asimptoticheskoe raspredelenie sobstvennykh znachenii ellipticheskikh operatorov”, Dokl. AN SSSR, 158:1 (1964), 41–44 | Zbl

[7] Lavrenchuk V. P., “Zagalni kpaiovi zadachi dlya parabolichnikh sistem zi zrostayuchimi koefitsientami”, Dopovsh AN URSR, Ser. A, 1968, 238–242 | Zbl