EXISTENCE AND BEHAVIOR OF SOLUTIONS FOR CONVECTION-DIFFUSION EQUATIONS WITH THIRD TYPE BOUNDARY CONDITION

In this paper, we study a nonlinear convection-diffusion type equation with initial and third type boundary condition in the general case. We obtain the sufficient conditions under which the existence and uniqueness of the generalized solution for the considered problem is proved. Moreover, we investigate the long-time behavior of the solution and prove the existence of absorbing sets in two different spaces.