Related papers: Scalar conservation laws on moving hypersurfaces
We investigate thermodynamics of static and spherically symmetric black holes (BHs) in the Horndeski theories. Because of the presence of the higher-derivative interactions and the nonminimal derivative couplings of the scalar field, the…
We propose a new numerical approach to compute nonclassical solutions to hyperbolic conservation laws. The class of finite difference schemes presented here is fully conservative and keep nonclassical shock waves as sharp interfaces,…
We consider conservation laws with nonlocal velocity and show for nonlocal weights of exponential type that the unique solutions converge in a weak or strong sense (dependent on the regularity of the velocity) to the entropy solution of the…
For hyperbolic systems of conservation laws in one space dimension with a mathematical entropy, we define the notion of entropy velocity. Then we give sufficient conditions for such a system to be covariant under the action of a group of…
This paper extends, to a class of systems of semi-linear hyperbolic second order PDEs in three variables, the geometric study of a single nonlinear hyperbolic PDE in the plane as presented in [Anderson I.M., Kamran N., Duke Math. J. 87…
We introduce the Stable Physics-Informed Kernel Evolution (SPIKE) method for numerical computation of inviscid hyperbolic conservation laws. SPIKE resolves a fundamental paradox: how strong-form residual minimization can capture weak…
Maximal parabolic $L^p$-regularity of linear parabolic equations on an evolving surface is shown by pulling back the problem to the initial surface and studying the maximal $L^p$-regularity on a fixed surface. By freezing the coefficients…
A new class of Hermite methods for solving nonlinear conservation laws is presented. While preserving the high order spatial accuracy for smooth solutions in the existing Hermite methods, the new methods come with better stability…
A novel structure-preserving numerical method to solve random hyperbolic systems of conservation laws is presented. The method uses a concept of generalized, measure-valued solutions to random conservation laws. This yields a linear partial…
When driven out of equilibrium by a temperature gradient, fluids respond by developing a nontrivial, inhomogeneous structure according to the governing macroscopic laws. Here we show that such structure obeys strikingly simple scaling laws…
We consider the local well-posedness of the one-dimensional nonisentropic Euler equations with moving physical vacuum boundary condition. The physical vacuum singularity requires the sound speed to be scaled as the square root of the…
The scaling of the exact solution of a hyperbolic balance law generates a family of scaled problems in which the source term does not depend on the current solution. These problems are used to construct a sequence of solutions whose…
We prove the stability with respect to the flux of solutions to initial-boundary value problems for scalar non-autonomous conservation laws in one space dimension. Key estimates are obtained through a careful construction of the solutions.
The paper is concerned with the boundary controllability of entropy weak solutions to hyperbolic systems of conservation laws. We prove a general result on the asymptotic stabilization of a system near a constant state. On the other hand,…
We present a graph-based numerical method for solving hyperbolic systems of conservation laws using discontinuous finite elements. This work fills important gaps in the theory as well as practice of graph-based schemes. In particular, four…
We study how conservation laws shape the spreading of quantum coherence in many-body dynamics. Focusing on $U(1)$-symmetric random circuits, charge-and-dipole conserving circuits, as well as ergodic Hamiltonian dynamics, we probe coherences…
Einstein equations are addressed with the energy-momentum tensor that appears if the equations under discussion are required to possess conformal invariance. It is proved that thus derived equations (equations of conformally invariant…
We discuss an alternative approach to the uniformisation problem on surfaces with boundary by representing conformal structures on surfaces $M$ of general type by hyperbolic metrics with boundary curves of constant positive geodesic…
In this continuum theory, we propose a mathematical framework to study the mechanical interplay of bulk-surfaces materials undergoing deformation and phase segregation. To this end, we devise a principle of virtual powers with a…
We prove sharp bounds on the enstrophy growth in viscous scalar conservation laws. The upper bound is, up to a prefactor, the enstrophy created by the steepest viscous shock admissible by the $L^\infty$ and total variation bounds and…