Higher-order for the multidimensional generalized bbm-burgers equation: Existence and convergence results

摘要

We study the global existence of solutions for the multidimensional generalized BBM-Burgers equations of the form u_t +∑ _(j=1)~dfj (u)_(xj)= δ ∑_(j=1)~du_(xjxt) + ∑_(j=1)~d(∑ _(n=1)~N(1)~(n+1)γ_n? _(xj)~(2n) μ, for (x,t) ∈ ? ~d ×?_+, with initial data u(x,0)=u _0(x), x ∈ ? ~d, as α>0, γ _n >0, n=1,?, N approach zero, and f is a sufficiently smooth function. We also deal with the convergence of solutions of this Cauchy problem, and the proofs are based instead on DiPerna's uniqueness theory for entropy measure-valued solutions.