An investigation of the behavior of $L_2$-norms of the solutions of strongly parabolic systems with dissipation
S. D. Èidel'man, F. O. Porper
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.
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Mathematics of the USSR-Izvestiya, 1973, 7:3, 675–689
MSC: Primary 35B35, 35K45; Secondary 35C15
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”, Izv. Akad. Nauk SSSR Ser. Mat., 37:3 (1973), 676–690; Math. USSR-Izv., 7:3 (1973), 675–689
Citation in format AMSBIB
\by S.~D.~\`Eidel'man, F.~O.~Porper
\paper An investigation of the behavior of $L_2$-norms of the solutions of strongly parabolic systems with dissipation
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\jour Math. USSR-Izv.
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