We propose a general framework for the study of L 1 contractive semigroups of solutions to
conservation laws with discontinuous flux: u_t+ f (x, u) _x= 0,\qquad f (x, u)=\left {f^ l (u), & x< …

We consider an immiscible incompressible two-phase flow in a porous medium composed
of two different rocks so that the capillary pressure field is discontinuous at the interface …

For the hyperbolic conservation laws with discontinuous-flux function, there may exist
several consistent notions of entropy solutions; the difference between them lies in the …

We consider the system of equations governing an incompressible immiscible two-phase
flow within a heterogeneous porous medium made of two different rock types. Since the …

Scalar conservation law∂ t ρ (t, x)+∂ x (f (t, x, ρ))= 0 with a flux C 1 in the state variable ρ,
piecewise C 1 in the (t, x)-plane admits infinitely many consistent notions of solution which …

The Strategic Research Agenda (SRA; https://www. ejp-eurad. eu/publications/eurad-sra) of
the European Joint Programme on Radioactive Waste Management (EURAD; https://www …

In this paper we show how one can construct families of continuous functions which satisfy
asymptotically scalar equations with discontinuous nonlinearity and systems having …

Conservation laws of the form∂ tu+∂ xf (x; u)= 0 with space-discontinuous flux f (x;⋅)= fl (⋅)
1 x< 0+ fr (⋅) 1 x> 0 were deeply investigated in the past ten years, with a particular …

Hyperbolic conservation laws of the form u t+ div f (t, x; u)= 0 with discontinuous in (t, x) flux
function f attracted much attention in last 20 years, because of the difficulties of adaptation of …

Abstract In Ahmed et al.(2019) a space–time domain decomposition method was proposed
for two-phase flow in a porous medium composed of two different rock types, so that the …