Displaying similar documents to “Smoothness effect and decay on a class of non linear evolution equation”

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...

Strichartz Type Estimates for Oscillatory Problems for Semilinear Wave Equation

Di Pomponio, Stefania (2000)

Serdica Mathematical Journal

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The author is partially supported by: M. U. R. S. T. Prog. Nazionale “Problemi e Metodi nella Teoria delle Equazioni Iperboliche”. We treat the oscillatory problem for semilinear wave equation. The oscillatory initial data are of the type u(0, x) = h(x) + ε^(σ+1) * e^(il(x)/ε) * b0 (ε, x) ∂t u(0, x) = ε^σ * e^(il(x)/ε) * b1(ε, x). By using suitable variants of Strichartz estimate we extend the results from [6] on a priori estimates of the approximations of...

Global existence and decay of solutions of a coupled system of BBM-Burgers equations.

Jardel Morais Pereira (2000)

Revista Matemática Complutense

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The global well-posedness of the initial-value problem associated to the coupled system of BBM-Burgers equations (*) in the classical Sobolev spaces H(R) x H(R) for s ≥ 2 is studied. Furthermore we find decay estimates of the solutions of (*) in the norm L(R) x L(R), 2 ≤ q ≤ ∞ for general initial data. Model (*) is motivated by a work due to Gear and Grimshaw [10] who considered strong interaction of weakly nonlinear long waves governed by a coupled system of KdV equations.