相关论文: Flux-conserving hyperbolic systems and two-dimensi…
We introduce a class of nonlinear hyperbolic conservation laws on a Schwarzschild black hole background and derive several properties satisfied by (possibly weak) solutions. Next, we formulate a numerical approximation scheme which is based…
This investigation is devoted to the solutions of Einstein's field equations for a circularly symmetric anisotropic fluid, with kinematic self-similarity of the first kind, in $(2+1)$-dimensional spacetimes. In the case where the radial…
We establish existence and uniqueness results for the singular initial value problem associated with a class of quasilinear, symmetric hyperbolic, partial differential equations of Fuchsian type in several space dimensions. This is an…
We propose in this work the first symmetric hyperbolic system of conservation laws to describe viscoelastic flows of Maxwell fluids, i.e. fluidswith memory that are characterized by one relaxation-time parameter. Precisely, the system of…
The two-dimensional CGHS model provides an interesting toy-model for the study of black hole evaporation. For this model, a quantum effective action, which incorporates Hawking radiation and backreaction, can be explicitly constructed. In…
Inflow BC plays a critical role in the study of hyperbolic PDE in a bounded domain. We establish $W^{1,\infty}$ stability for 1D hyperbolic conservation laws with inflow data in a bounded interval, and $W^{2,3+}$ stability of a large class…
We analyze the flux conservation property of the finite element method. It is shown that the finite element solution does approximate the flux locally in the optimal order, i.e., the same order as that of the nodal interpolation operator.…
In this chapter, we aim at presenting the basic techniques necessary to go beyond the widely accepted paradigm of second-order numerics. We specifically focus on finite-volume schemes for hyperbolic conservation laws occuring in fluid…
Aim of these notes is provide a brief review of the current well-posedness theory for hyperbolic systems of conservation laws in one space dimension, also pointing out open problems and possible research directions. They supplement the…
We introduce a class of one dimensional deterministic models of energy-volume conserving interfaces. Numerical simulations show that these dynamics are genuinely super-diffusive. We then modify the dynamics by adding a conservative…
A pedagogical discussion is given of some aspects of \lq\lq quantum black holes", primarily using recently developed two-dimensional models. After a short preliminary concerning classical black holes, we give several motivations for…
We study black hole formation and evaporation in a four-dimensional semiclassical model that preserves diffeomorphism invariance and reproduces the one-loop trace anomaly. Solving the quantum-corrected Einstein equations for the collapse of…
Black hole evaporation is investigated in a (1+1)-dimensional model of quantum gravity. Quantum corrections to the black hole entropy are computed, and the fine-grained entropy of the Hawking radiation is studied. A generalized second law…
We present new accretion solutions of a polytropic perfect fluid onto an f(R)-gravity de Sitter-like black hole. We consider two f(R)-gravity models and obtain finite-period cyclic flows oscillating between the event and cosmological…
This paper introduces a novel wave front tracking framework for reconstructing unknown flux functions in $2\times 2$ hyperbolic conservation laws, extending beyond the well-studied scalar case. By analyzing Riemann solutions at fixed…
We consider the coupling between the equations of motion of an inviscid compressible fluid in space with an objective Cattaneo-type extension for the heat flux. These equations are written in quasilinear form and we determine which of the…
We study the evaporation of black holes in space-times with extra dimensions of size L. We first obtain a potential which describes the expected behaviors of very large and very small black holes and then show that a (first order) phase…
Some of recent important developments are overviewed, several longstanding open problems are discussed, and a perspective is presented for the mathematical theory of multidimensional conservation laws. Some basic features and phenomena of…
It has been claimed that extreme black holes exhibit a phenomenon of flux expulsion for abelian Higgs vortices, irrespective of the relative width of the vortex to the black hole. Recent work by two of the authors showed a subtlety in the…
We exploit some common features of black hole and domain wall solutions of (super)gravity theories coupled to scalar fields and construct a class of stable extremal black holes that are non-BPS, but still can be described by first-order…