Geodesic
Diffeomorphisms of function spaces corresponding to quasilinear parabolic equations
Sbornik. Mathematics, Tome 45 (1983) no. 3, pp. 359-378

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This paper considers a boundary value problem for a quasilinear parabolic equation. In terms of Sobolev and Besov spaces the author determines a solution space $A$ and a space $B$ of initial conditions and right hand members such that the operator corresponding to the boundary value problem is a diffeomorphism, analytic in the Frechet sense, of the whole space $A$ and a domain $\mathscr O$ in the space $B$. The behavior of the inverse operator of the problem around the boundary of $\mathscr O$ is studied, and it is shown that for different problems the domain $\mathscr O$ can coincide with the whole function space or be a strict subset of it. Bibliography: 13 titles. 
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     author = {S. B. Kuksin},
     title = {Diffeomorphisms of function spaces corresponding to quasilinear parabolic equations},
     journal = {Sbornik. Mathematics},
     pages = {359--378},
     publisher = {mathdoc},
     volume = {45},
     number = {3},
     year = {1983},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1983_45_3_a2/}
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S. B. Kuksin. Diffeomorphisms of function spaces corresponding to quasilinear parabolic equations. Sbornik. Mathematics, Tome 45 (1983) no. 3, pp. 359-378. http://geodesic.mathdoc.fr/item/SM_1983_45_3_a2/