Existence of entropy solutions for some strongly nonlinear p(x)-parabolic problems with L1-data
Abstract
This paper is devoted to study the following strongly nonlinear p(x)-parabolic problem
du/d t- div a(x,t,\nabla u) + g(x,t,u,\nabla u) + \delta|u|^{p(x)-2}u = f - div \phi(u) in Q_T,
u = 0 on \Sigma_{T},
u(x,0)= u_0 in \Omega,
with f \in L^{1}(Q_T), \phi\in C^{0}(IR,IR^{N}), u_0 \in L^{1}(\Omega) and \delta>0. We prove the existence of entropy solutions for this problem in the parabolic space with variable exponent V.
du/d t- div a(x,t,\nabla u) + g(x,t,u,\nabla u) + \delta|u|^{p(x)-2}u = f - div \phi(u) in Q_T,
u = 0 on \Sigma_{T},
u(x,0)= u_0 in \Omega,
with f \in L^{1}(Q_T), \phi\in C^{0}(IR,IR^{N}), u_0 \in L^{1}(\Omega) and \delta>0. We prove the existence of entropy solutions for this problem in the parabolic space with variable exponent V.
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PDFDOI: https://doi.org/10.52846/ami.v42i2.622