In this paper, we investigate the existence of solutions to a nonlinear parabolic system, which couples a non-homogeneous reaction-diffusion-type equation and a non-homogeneous viscous Hamilton–Jacobi one. The initial data and right-hand sides satisfy suitable integrability conditions and non-negative. To simplify the presentation of our results, we will consider separately two simplified models : first, vanishing initial data, and then, vanishing right-hand sides.

中文翻译：

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一类涉及势和梯度项的非线性抛物系统的存在性结果

在本文中，我们研究了非线性抛物方程组解的存在性，该方程组耦合了一个非齐次反应扩散方程和一个非齐次粘性哈密顿-雅各比方程。初始数据和右侧均满足适当的可积性条件且非负。为了简化结果的表示，我们将分别考虑两个简化的模型：首先，消失初始数据，然后消失右手边。