Low energy $\overline{K}N$ interactions are studied within unitary chiral perturbation theory at next-to-leading order with ten coupled channels. We pay special attention to the recent precise determination of the strong shift and width of the kaonic hydrogen $1s$ state by the DEAR Collaboration that has challenged our theoretical understanding of this sector of strong interactions. We typically find two classes of solutions, both of them reproducing previous data, that either can or cannot accommodate the DEAR measurements. The former class has not been previously discussed.

In this paper we provide analytical and/or numerical evidences of the qualitative properties of discontinuity fronts, developed by the solutions of the relativistic heat equation (and some porous media variants). We study the local-in-time existence of radially symmetric smooth solutions (inside the support) for smooth initial conditions whose only discontinuities are at the boundary of its support. Then we show some numerical experiments that permit us to conjecture the regularity and qualitative properties of entropy solutions of the relativistic heat equation and some porous media–type variants.

A Reply to the Comment by B. Borasoy, R. Nissler, and W. Weise.