Asymptotic profiles of solutions to convection-diffusion equations

We compare our result with the classical representation in terms of (super)quadratic BSDEs, and show in particular that existence of a viscosity solution to the viscous HJ equation

It is known that, for a lower semicontinuous (for short l.s.c.) proper convex function f on a Hilbert space, its Moreau–Yosida regularization f ε is of class C 1 and converges to f as

For results concerning long time behaviour of solutions of Hamilton-Jacobi equations, one can for example refer to the papers [1] and [6], see also [2].. Remark 2 Notice that

We extend our estimates to equations on complete non compact manifolds satisfying a lower bound estimate on the Ricci curvature, and derive some Liouville type theorems..

Extensions to the case of unbounded solutions for first-order equations in the non-periodic case is consider in the paper of Roquejoffre with the first author ([6]) : the existence

Lauren¸cot, Very singular solutions to a nonlinear parabolic equation with absorption, II- Uniqueness, Proc.. Lauren¸cot, Global solutions to viscous Hamilton-Jacobi equations

V´eron, The boundary trace and generalized boundary value problem for semilinear elliptic equations with coercive absorption, Comm. Stein, Singular integrals and

MURAT, Uniqueness and the maximum principle for quasilinear elliptic equations with quadratic growth conditions, Arch.. Ra-