Zill & Cullen's text was helpful for me. (Score 1)

Zill & Cullen's "Differential Equations with Boundary Value Problems" has good PDE applications (9th chapter onwards), including the heat/wave/etc. equations mentioned. It should be a good starting point to bridge where you currently are with a physical basis (they uncover what the equations physically represent with some mini-derivations). I used 4th ed. I would be surprised if Arfken didn't hit this.