فهرست نشریات علمی دسترسی آزاد ایران

In this work, we study the existence of an initial boundary problem of a quasilinear parabolic problem with variable exponent  and  $ L ^{1} $-data of the type\begin{equation*}\left\{\begin{array}{ll}(b(u))_{t}-\text{div}(\left\vert \nabla u\right\vert ^{p(x)-2}\nabla u)+\lambda\left\vert u\right\vert ^{p(x)-2}u=f(x,t,u) \text{ } &\text{in}\hspace{0.5cm}Q=\Omega \times ]0,T[, \\u=0 & \text{on}\hspace{0.5cm}\Sigma =\partial \Omega \times ]0,T[, \\b(u)(t=0)=b(u_{0}) & \text{in}\hspace{0.5cm}\Omega , \end{array}\right.\end{equation*}where $ \lambda>0$ and $ T $ is positive constant. The main contribution of our work is to prove the existence of a renormalized solution. The functional setting involves Lebesgue– Sobolev spaces with variable exponents.