The book is devoted to the theory of gradient flows in the general framework of metric
spaces, and in the more specific setting of the space of probability measures, which provide …

This text is concerned with the quantitative aspects of the theory of nonlinear diffusion
equations; equations which can be seen as nonlinear variations of the classical heat …

In this paper, we study an initial-boundary value problem for the following mixed pseudo-
parabolic p-Laplacian type equation with logarithmic nonlinearity in a bounded domain Ω⊂ …

We consider the initial boundary value problem for a mixed pseudo-parabolic p-Laplacian
type equation with logarithmic nonlinearity. Constructing a family of potential wells and using …

Recently, in [26], an interesting connection between the p-harmonic functions and the 1/H
hypersurface flow (also called the inverse mean curvature flow) was established. Let v be a …

In a finite-dimensional smooth setting, the gradient flow of a function φ: M d→ ℝ defined on a
Riemannian manifold M d simply means the family of solutions u: ℝ→ M d of the Cauchy …

In this paper, we study the following parabolic problem of Kirchhoff type with logarithmic
nonlinearity:{u_t+ M (u^ 2_s) L _Ku=| u|^ p-2 u\log| u|,\in Ω * (0,+ ∞),\\displaystyle u (x, t)= 0 …

We show that the L p Busemann–Petty centroid inequality provides an elementary and
powerful tool to the study of some sharp affine functional inequalities with a geometric …

We show here that decay estimates can be derived simply by integral inequalities. This
result allows us to prove these kind of estimates, with an unified proof, for different nonlinear …

We consider the stability of the functional inequalities concerning the entropy functional. For
the Boltzmann–Shannon entropy, the logarithmic Sobolev inequality holds as a lower bound …