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JOURNALS // Matematicheskii Sbornik // Archive

Mat. Sb. (N.S.), 1977 Volume 104(146), Number 4(12), Pages 535–558 (Mi sm2964)

This article is cited in 11 papers

On the stability of stationary solutions of nonlinear parabolic systems

V. S. Belonosov, M. P. Vishnevskii


Abstract: In this paper the linearization method is developed for the problem of stability of stationary solutions of nonlinear autonomous parabolic systems of general form. Estimates, uniform with respect to time, are established for Hölder norms of the solutions of the linearized systems. These estimates are then used in the study of the nonlinear problems. Theorems are proved concerning the stability of the first approximation and the conditional stability, generalizing the well-known Lyapunov theorems from the theory of ordinary differential equations.
Bibliography: 11 titles.

UDC: 517.946

MSC: Primary 35B35, 35K55; Secondary 35B45

Received: 13.06.1977


 English version:
Mathematics of the USSR-Sbornik, 1977, 33:4, 465–484

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