This paper deals with the numerical approximation of the mild solution of a quasilinear parabolic equation with variable exponent. Under some conditions, it is shown that the mild solution is a weak solution. Numerical tests are performed using the split Bregman method. The functional setting involves Lebesgue and Sobolev spaces with variable exponent.

Leray-Lions operator with variable exponent; parabolic equation; numerical; iterative method; mild solution