Geodesic
Quasistationary trajectories of semilinear dynamical equations of Sobolev type
Izvestiya. Mathematics , Tome 42 (1994) no. 3, pp. 601-614

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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. 
@article{IM2_1994_42_3_a5,
     author = {G. A. Sviridyuk},
     title = {Quasistationary trajectories of semilinear dynamical equations of {Sobolev} type},
     journal = {Izvestiya. Mathematics },
     pages = {601--614},
     publisher = {mathdoc},
     volume = {42},
     number = {3},
     year = {1994},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1994_42_3_a5/}
}
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G. A. Sviridyuk. Quasistationary trajectories of semilinear dynamical equations of Sobolev type. Izvestiya. Mathematics , Tome 42 (1994) no. 3, pp. 601-614. http://geodesic.mathdoc.fr/item/IM2_1994_42_3_a5/