An asymptotic supnorm estimate for solutions of 1-D systems of convection-diffusion equations

作者：Braz e Silva P; Melo Wilberclay G; Zingano Paulo R

来源：Journal of Differential Equations, 2015, 258(8): 2806-2822.

DOI：10.1016/j.jde.2014.12.026

We show how to use the L-p-L-q approach to obtain fundamental estimates for the spatial supnorm values of solutions u(x,t) = (u(1)(x, t), ... u(m) (x, t)) to general systems of convection-diffusion equations of the form
partial derivative u(i)/partial derivative(t) + partial derivative/partial derivative x f(i) (x, t, u(1),...,u(m)) + partial derivative/partial derivative x g(i) (t, u(i)) = mu(i)(t) partial derivative 2(i)(u)/partial derivative x(2), 1 <= i <= m,
with initial data u(., 0) is an element of L-P0 (R) boolean AND L-infinity(R) for some 1 <= P-0 < infinity, where mu(i) (t) > 0, given arbitrary f = (f(1),..., f(m)), g = (g(1),..., g(m)) such that [f (x, t, u)vertical bar <= B(t)vertical bar u vertical bar for all x is an element of R, t >= 0, u is an element of Rm, where B is an element of C-0([0, infinity]).

• 出版日期2015-4-15