Bir Sınıf Doğrusal Olmayan Difüzyon-Konveksiyon Denklemlerinin İncelenmesi

Abstract

In this dissertation, the solvability, uniqueness and long-time behavior of solution of the nonlinear diffusion-convection equation with 3. type boundary condition have been investigated. Firstly, when the initial condition is zero, the problem is investigated in sublinear, linear and super linear cases, depending on the nonlinear part. In these three cases, for the solvability of the solution, sufficient conditions are obtained. Under these conditions, existence of the generalized solution is proved using a general theorem. When the initial condition is nonzero, the existence of the generalized solution is proved in sublinear, linear and super linear cases using the same method. Additionally, the uniqueness of the solution is investigated.Finally, when equation and boundary condition are homogeneous, some results are obtained on the behavior of the solution. Then, in the nonhomogeneous, autonomous case, the existence of the absorbing sets in two different spaces are proved.