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We consider the Cauchy problem for the generalizedZakharov--Kuznetsov--Burgers equation in 2D. This is one of the nonlineardispersive-dissipative equations, which has a spatial anisotropic dissipativeterm $-\mu u_{xx}$. In this paper, we prove that the solution to this problemdecays at the rate of $t^{-\frac{3}{4}}$ in the $L^{\infty}$-sense, providedthat the initial data $u_{0}(x, y)$ satisfies $u_{0}\in L^{1}(\mathbb{R}^{2})$and some appropriate regularity assumptions. Moreover, we investigate the moredetailed large time behavior and obtain a lower bound of the $L^{\infty}$-normof the solution. As a result, we prove that the given decay rate$t^{-\frac{3}{4}}$ of the solution to be optimal. Furthermore, combining thetechniques used for the parabolic equations and for theSchr$\ddot{\mathrm{o}}$dinger equation, we derive the explicit asymptoticprofile for the solution.

Optimal Decay Estimate and Asymptotic Profile for Solutions to the Generalized Zakharov--Kuznetsov--Burgers Equation in 2D