The Cauchy-Dirichlet problem for the anisotropic parabolic equation with variable exponents in the presence of a nonlinear source and gradient term is considered. We prove the existence and uniqueness of a weak solution that is Lipschitz continuous in the space variables.

中文翻译：

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关于指数随时间变化的拟线性各向异性抛物线方程

考虑了存在非线性源和梯度项时具有可变指数的各向异性抛物线方程的柯西-狄利克雷问题。我们证明了在空间变量中 Lipschitz 连续的弱解的存在性和唯一性。