J. Endal

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math.AP2025

Nonlocal degenerate parabolic hyperbolic equations on bounded domains

NathaÃ«l Alibaud, JÃ¸rgen Endal, Espen Jakobsen +1

We study well-posedness of degenerate mixed-type parabolic-hyperbolic equations $\partial_{t} u + div (f (u)) = L [b (u)]$ on bounded domains with general Dirichl…

math.AP2025

Nonlocal degenerate parabolic hyperbolic equations on bounded domains. Part II: Existence

JÃ¸rgen Endal, Espen R Jakobsen, Ola MÃ¦hlen

We study well-posedness of degenerate mixed-type parabolic-hyperbolic equations $\partial_{t} u + div (f (u)) = L [b (u)]$ on bounded domains with general Diric…

math.AP2024

Optimal stability results and nonlinear duality for $L^{\infty}$ entropy and $L^{1}$ viscosity solutions

NathaÃ«l Alibaud, JÃ¸rgen 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…

Nonlocal degenerate parabolic hyperbolic equations on bounded domains

Nonlocal degenerate parabolic hyperbolic equations on bounded domains. Part II: Existence

Optimal stability results and nonlinear duality for L∞ entropy and L1 viscosity solutions

Optimal stability results and nonlinear duality for $L^{\infty}$ entropy and $L^{1}$ viscosity solutions