37 citations · 56 across the 7 of their papers we have counts for
9 papers
Nonlocal degenerate parabolic hyperbolic equations on bounded domains
Nathaël Alibaud, Jørgen Endal, Espen Jakobsen +1
We study well-posedness of degenerate mixed-type parabolic-hyperbolic equations on bounded domains with general Dirichl…
(Bounded) Traveling Combustion Fronts With Degenerate Kinetics
Nathaël Alibaud, Gawtum Namah
We consider the propagation of a flame front in a solid periodic medium. The model is governed by a free boundary system in which the front's velocity depends on the temperature vi…
Nonlocal Dissipation Measure and L 1 Kinetic Theory For Fractional Conservation Laws
Nathaël Alibaud, Boris Andreianov, Adama Ouedraogo
We introduce a kinetic formulation for scalar conservation laws with nonlocal and nonlinear diffusion terms. We deal with merely L 1 initial data, general self-adjoint pure jump L{…
Optimal stability results and nonlinear duality for entropy and viscosity solutions
Nathaël Alibaud, Jørgen Endal, Espen Robstad Jakobsen
We give a new and rigorous duality relation between two central notions of weak solutions of nonlinear PDEs: entropy and viscosity solutions. It takes the form of the nonlinear dua…
Characterization of nonlocal diffusion operators satisfying the Liouville theorem. Irrational numbers and subgroups of
Nathaël Alibaud, Félix del Teso, Jørgen Endal +1
We investigate the characterization of generators of Lévy processes satisfying the Liouville theorem: Bounded functions solving are constant. T…
On the propagation of a periodic flame front by an arrhenius kinetic
Nathaël Alibaud, Gawtum Namah
We consider the propagation of a flame front in a solid medium with a periodic structure. The model is governed by a free boundary system for the pair" temperature-front. "The fron…
Optimal continuous dependence estimates for fractional degenerate parabolic equations
Nathael Alibaud, Simone Cifani, Espen Jakobsen
We derive continuous dependence estimates for weak entropy solutions of degenerate parabolic equations with nonlinear fractional diffusion. The diffusion term involves the fraction…
Continuous dependence estimates for nonlinear fractional convection-diffusion equations
Nathaël Alibaud, Simone Cifani, Espen R. Jakobsen
We develop a general framework for finding error estimates for convection-diffusion equations with nonlocal, nonlinear, and possibly degenerate diffusion terms. The equations are n…
Asymptotic properties of entropy solutions to fractal Burgers equation
Nathaël Alibaud, Cyril Imbert, Grzegorz Karch
We study properties of solutions of the initial value problem for the nonlinear and nonlocal equation u_t+(-\partial^2_x)^{α/2} u+uu_x=0 with alpha in (0,1], supplemented with an i…