Quasistationary trajectories of semilinear dynamical equations of Sobolev type

G. A. Sviridyuk

Izvestiya. Mathematics , Tome 42 (1994) no. 3, pp. 601-614.

Résumé

The unique solvability of the Cauchy problem $u(0)=u_0$ for an operator differential equation $L\dot u=M(u)$ is investigated in the case of $L$-boundedness of the operator $M_{u_0}'$ . The results obtained are illustrated on the Cauchy–Dirichlet problem for the Hoff equation and for Oskolkov's system of equations.

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