I went to a talk today and the speaker mentioned when you add a Laplacian term to a PDE, the Laplacian will dominate (in what sense?), which I don't quite understand. I know this question is a bit vague but I appreciate if someone could clarify the question more.

I went to a talk today and the speaker mentioned when you add a Laplacian term to a PDE, the Laplacian will dominate (in what sense?), which I don't quite understand. I know this question is a bit vague but I appreciate if someone could clarify the question more.

Update: The speaker didn't actually mention specific pdes. He said it's more like a general "rule" or principle. Since he said it like a convention, I didn't have gut to ask him this question. I understand there are exceptions and I appreciate if there are common pdes that follow his "principle".