SINGULAR PERTURBATIONS FOR A CLASS OF DEGENERATE INEQUALITIES THE FRAMEWORK OF FUNCTIONS WITH BOUNDED VARIATIONS

Abstract. We study the limit as goes to 0+ for the sequence (u)>0 of solutions to the Dirichlet problem for the quasilinear parabolic operators H(t, x,.) : u → ∂tu + p∑ i=1 ∂xiϕi(t, x, u) + ψ(t, x, u) − ∆φ(u), where φ is a nondecreasing function, associated with a positiveness condition in an open bounded domain of Rp, 1 ≤ p < +∞. The positive parameter being fixed, we first pro-pose the definition of a weak entropy solution, the boundary conditions being expressed through the mathematical framework of the Divergence-Measure fields. Then, the unique-ness proof for refers to the technique of doubling the variables and the existence property is obtained through the artificial viscosity method. Lastly, a BV ∩ L∞-estimate for the sequence (u)>0 is used to take the limit with