Existência global de soluções para certos sistemas parabólicos não lineares.

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Date
2005-03-02Author
Webler, Claudete Matilde
http://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4744427P6
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In this work, we study the global existence of smooth solutions for certain
systems of the form ut + f(u)x = Duxx, where u and f are vectors and D
is a positive, constant and diagonalizable matrix. We assume that the initial
condition u0 satisfies jju0¡ujjL1(IR) < r, where u is a fixed vector, f is defined
in the ball of the center u of radius r and jju0¡ujjL2(IR) is su±ciently small. We
show how our results apply to the equations of gas dynamics and we include a
result which shows that for the Navier-Stokes equations of compressible flow,
smoothing of initial discontinuities must occur for velocity and energy, but not
for the density.