Existence Results to a Class of Nonlinear Parabolic Systems Involving Potential and Gradient Terms
Abstract
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. In order to simplify the presentation of our results, we will consider separately two simplified models : first, vanishing initial data, and then, vanishing right-hand sides.
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