This paper is concerned with the study of the nonlinear Dirichlet parabolic problem in a bounded subset \(\Omega \subset I\!\!R^N\)

where A is an operator of Leray-Lions type acted from the parabolic anisotropic space \(L^{\vec {p}}(0,T;W_{0}^{1,\vec {p}}(\Omega ))\) into its dual. g is a nonlinear term having a growth condition with respect to \(\nabla u\) and satisfying a sign condition with no growth condition with respect to u. In addition, when the initial condition \(u_{0}\) and the data f are assumed to be merely integrable and \(\phi (\cdot )\in C^{0}(I\!\!R,I\!\!R^{N}),\) we prove the existence of entropy solutions for this class of problems.

本文关注的是有界子集\(\Omega\subset I\!\!R^N\)中非线性Dirichlet抛物线问题的研究

其中A是 Leray-Lions 类型的算子，作用于抛物线各向异性空间\(L^{\vec {p}}(0,T;W_{0}^{1,\vec {p}}(\Omega ) )\)成它的对偶。g是一个非线性项，它具有关于\(\nabla u\) 的增长条件，并且满足一个关于u没有增长条件的符号条件。此外，当初始条件\(u_{0}\)和数据f仅被假定为可积且\(\phi (\cdot )\in C^{0}(I\!\!R,I \!\!R^{N}),\)我们证明了这类问题的熵解的存在性。