Herein, we propose a mathematical model for road crack segmentation in images, focusing on the difficul- ties of the real world road conditions, such as the lighting and color changes, complex crack shape etc. The proposed model belongs to the family of nonlinear partial differential equations (PDEs), involving edge-aware anisotropic diffu- sion, curvature-driven contour evolution, high order biharmonic regularization, and feature-driven attraction force for capturing the crack regions. A theoretical analysis is conducted to show the well-posedness of the model. In addition, a physics-informed neural network (PINN) version of the model is presented which allows us to discretize the PDEs in a mesh-free fashion and to approximate high order derivatives through the deep neural networks. Various numerical experi- ments on EdmCrack600 data are implemented for validating the proposed method. All the experimental results show that the proposed model is superior to the other segmentation models, and that our model achieves excellent performance in terms of the metrics, i.e., dice similarity, intersection over union, sensitivity, and specificity.