We study the effect of p-Laplacian operator in modelling heat equation through a porous medium $$\Lambda _\epsilon \subset {\mathbb {R}}^N$$ ( $$N\ge 2$$ ). The case $$p=2$$ was recently published Anguiano (Mediterr J Math 17:18, https://doi.org/10.1007/s00009-019-1459-y , 2020). Using rigorous functional analysis techniques and properties Sobolev spaces, we managed to solve additional (nontriv...