We study two equations of Lotka-Volterra type that describe the Darwinian evolution of a
population density. In the first model a Laplace term represents the mutations. In the second …

We study in the present article the Kardar–Parisi–Zhang (KPZ) equation ∂ _t h (t, x)= ν Δ h
(t, x)+ λ| ∇ h (t, x)|^ 2+ D\, η (t, x),\qquad (t, x) ∈ R _+ * R^ d∂ th (t, x)= ν Δ h (t, x)+ λ|∇ h (t …

We investigate the dynamics of a limit of interacting FitzHugh--Nagumo neurons in the
regime of large interaction coefficients. We consider the dynamics described by a mean-field …

We provide deficit estimates for Nelson's hypercontractivity inequality, the logarithmic
Sobolev inequality, and Talagrand's transportation cost inequality under the restriction that …

We provide some new integral estimates for solutions to Hamilton-Jacobi equations and we
discuss several consequences, ranging from $ L^ p $-rates of convergence for the vanishing …

We study the nonnegative solutions of the viscous Hamilton–Jacobi problem {ut− ν Δ u+|∇
u| q= 0, u (0)= u 0, in Q Ω, T= Ω×(0, T), where q> 1, ν≧ 0, T∈(0,∞], and Ω= RN or Ω is a …

Here we study the nonnegative solutions of the viscous Hamilton--Jacobi equation u_ t-Δ u+|
∇ u|^ q= 0 in Q_Ω,T=Ω*\left(0,T\right), where q>1, T∈\left(0,∞\right, and Ω is a smooth …

The one-dimensional viscous conservation law is considered on the whole line $$ u_t+ f (u)
_x=\eps u_ {xx},\quad (x, t)\in\RR\times\overline {\RP},\quad\eps> 0, $$ subject to positive …

We study in this series of articles the Kardar-Parisi-Zhang (KPZ) equation $$\partial_t h (t,
x)=\nu\Delta h (t, x)+\lambda V (|\nabla h (t, x)|)+\sqrt {D}\,\eta (t, x),\qquad x\in {\mathbb {R}} …

In this article we study the initial trace problem for the nonnegative solutions of equation ut−
Δu+|∇ u| q= 0 in QΩ, T= Ω×(0, T), where q> 0, and Ω= ℝN, or Ω is a bounded domain of ℝN …