Continuous dependence of renormalized solution for convection-diffusion problems involving a nonlocal operator
Abstract
In Ouédraogo A. et al (cf. [30]), it is provided existence and uniqueness results
of L^1-renormalized entropy solution for the Cauchy problem associated to the following vast class of nonlinear anisotropic degenerate parabolic-hyperbolic equations involving a nonlocal diffusion term:
∂_t u + ∇∙F(u) - ∑_(i,j=1)^N ∂_(x_i x_j)^2 A_ij (u) -L_μ [u] = f(u) in Q = (0; T) xR^N with T > 0 and N ≥ 1.
Our goal is to complement this previous work with a continuous dependence result of the L^1-solution with respect to the data set (F; a; μ; f; u0). The strategy is to follow the approach developed by Karlsen and Ulusoy in [28]. However, we must manage the diculties due to the fact that we are working in the whole space RN with an only integrable initial datum u0 and the term source f depends on the unknown function u.
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