On a Convection Diffusion Equation with Absorption Term

The paper studies the posedness of the convection diffusion equation u(t) = div (vertical bar del u(m)vertical bar(p-2) del u(m)) + Sigma(N)(i=1) partial derivative b(i) (u(m))/partial derivative X-i - u(mr) . with homogeneous boundary condition and with the initial value u(0)(X) is an element of Lq-1+1/m (Omega). By considering its regularized problem, using Moser iteration technique, the local bounded properties of the L-infinity-norm of u(k) and that of the L-p-norm of the gradient. del u(k) are got, where u(k) is the solution of the regularized problem of the equation. By the compactness theorem, the existence of the solution of the equation itself is obtained. By using some techniques in Zhao andYuan (Chin Ann MathA16(2): 179-194, 1995), the stability of the solutions is obtained too.