Anisotropic Degenerate Parabolic Problems in $$\mathbb {R}^N$$ R N with Variable Exponent and Locally Integrable Data

Abstract

In this paper, we prove the existence and regularity of weak solutions for a class of nonlinear anisotropic parabolic equations in the whole $$(0,T)\times \mathbb {R}^N$$ with $$p_i(x)$$ growth conditions and locally integrable data. The functional setting involves Lebesgue–Sobolev spaces with variable exponents. Our results are generalizations of the corresponding results in the constant exponent case and some results given in Bendahmane et al. (Commun Pure Appl Anal 12:1201–1220, 2013).