Displaying similar documents to “Cauchy problem for some semilinear evolution equations”

The Cauchy problem for systems through the normal form of systems and theory of weighted determinant

Waichiro Matsumoto (1998-1999)

Séminaire Équations aux dérivées partielles

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The author propose what is the principal part of linear systems of partial differential equations in the Cauchy problem through the normal form of systems in the meromorphic formal symbol class and the theory of weighted determinant. As applications, he choose the necessary and sufficient conditions for the analytic well-posedness ( Cauchy-Kowalevskaya theorem ) and C well-posedness (Levi condition).

Cauchy problem for semilinear parabolic equations with initial data in H (R) spaces.

Francis Ribaud (1998)

Revista Matemática Iberoamericana

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We study local and global Cauchy problems for the Semilinear Parabolic Equations ∂U - ΔU = P(D) F(U) with initial data in fractional Sobolev spaces H (R). In most of the studies on this subject, the initial data U(x) belongs to Lebesgue spaces L(R) or to supercritical fractional Sobolev spaces H (R) (s > n/p). Our purpose is to study the intermediate cases (namely for 0 < s < n/p). We give some mapping properties for functions with polynomial...