相关论文: Quasi-linear symmetric hyperbolic Fuchsian systems…

We prove propagation of weighted Sobolev regularity for solutions of the hyperboloidal Cauchy problem for a class of quasi-linear symmetric hyperbolic systems, under structure conditions compatible with the Einstein-Maxwell equations in…

We consider a class of Fuchsian equations that, for instance, describes the evolution of compressible fluid flows on a cosmological spacetime. Using the method of lines, we introduce a numerical algorithm for the singular initial value…

This paper is devoted to studying a multi-objective control problem for a class of multi-dimensional quasi-linear parabolic equations. The considered system is driven by a leader control and two follower controls. For each leader control, a…

In this paper, we study diagonal hyperbolic systems in one space dimension. Based on a new gradient entropy estimate, we prove the global existence of a continuous solution, for large and non-decreasing initial data. We remark that these…

We consider the well-posedness of a class of hyperbolic partial differential equations on a one dimensional spatial domain. This class includes in particular infinite-dimensional networks of transport, wave and beam equations, or even…

We study necessary conditions and sufficient conditions for the existence of local-in-time solutions of the Cauchy problem for superlinear fractional parabolic equations. Our conditions are sharp and clarify the relationship between the…

We establish a monotonicity property in the space variable for the solutions of an initial boundary value problem concerned with the parabolic partial differential equation connected with super-Brownian motion.

The boundary at infinity of a quasifuchsian hyperbolic manifold is equiped with a holomorphic quadratic differential. Its horizontal measured foliation $f$ can be interpreted as the natural analog of the measured bending lamination on the…

We study first-order symmetrizable hyperbolic $N\times N$ systems in a spacetime cylinder whose lateral boundary is totally characteristic. In local coordinates near the boundary at $x=0$, these systems take the form \[ \partial_t u +…

We prove some sharp regularity results for solutions of classical first order hyperbolic initial boundary value problems. Our two main improvements on the existing litterature are weaker regularity assumptions for the boundary data and…

Quasifuchsian hyperbolic manifolds, or more generally convex co-compact hyperbolic manifolds, have infinite volume, but they have a well-defined ``renormalized'' volume. We outline some relations between this renormalized volume and the…

In this paper we establish a relation between two exactly-solvable problems on one-dimensional hyperbolics space, namely singular Coulomb and singular oscillator systems.

This paper establishes the equivalence between systems described by a single first-order hyperbolic partial differential equation and systems described by integral delay equations. System-theoretic results are provided for both classes of…

Aim of this paper is to review some basic ideas and recent developments in the theory of strictly hyperbolic systems of conservation laws in one space dimension. The main focus will be on the uniqueness and stability of entropy weak…

We study the classical properties of a supersymmetric system which is often used as a model for supersymmetric quantum mechanics. It is found that the classical dynamics of the bosonic as well as the fermionic degrees of freedom is fully…

This paper investigates a novel mechanism for quasi-singularity formation in both linear and nonlinear hyperbolic wave equations in two and three dimensions. We prove that over any finite time interval, there exist inputs such that the…

In this paper we consider an initial boundary value problem for a semilinear parabolic equation with nonlinear nonlocal boundary condition. We prove comparison principle, the existence theorem of a local solution and study the problem of…

We study local and global existence of solutions for some semilinear parabolic initial boundary value problems with autonomous nonlinearities having a "Newtonian" nonlocal term.

We consider nonlinear perturbations of the hyperbolic equation in the Hilbert space. Necessary and sufficient conditions for the existence of solutions of boundary-value problem for the corresponding equation and iterative procedures for…

The purpose of this article is to study quasi linear parabolic partial differential equations of second order, posed on a bounded network, satisfying a nonlinear and non dynamical Neumann boundary condition at the vertices. We prove the…