Related papers: Completely linear degeneracy for quasilinear hyper…
We present a generalization of Kruzkov's theory to manifolds. Nonlinear hyperbolic conservation laws are posed on a differential (n+1)-manifold, called a spacetime, and the flux field is defined as a field of n-forms depending on a…
Hyperbolic metamaterials were originally introduced to overcome the diffraction limit of optical imaging. Soon thereafter it was realized that hyperbolic metamaterials demonstrate a number of novel phenomena resulting from the broadband…
We consider a class of semi-linear dissipative hyperbolic equations in which the operator associated to the linear part has a nontrivial kernel. Under appropriate assumptions on the nonlinear term, we prove that all solutions decay to 0, as…
We demonstrate that linear degeneracy is a necessary condition for quasilinear systems of Jordan block type to possess first-order Hamiltonian structures. Multi-Hamiltonian formulation of linearly degenerate systems governing…
Motivated by a new kind of initial boundary value problem (IBVP) with a free boundary arising in wave-structure interaction, we propose here a general approach to one-dimensional IBVP as well as transmission problems. For general strictly…
In this paper we derive a new first-order theory of relativistic dissipative fluids by adopting the trace-fixed particle frame. Whereas in a companion letter we show that this theory is hyperbolic, causal and stable at global equilibrium…
Coupled wave equations are popular tool for investigating longitudinal dynamical effects in semiconductor lasers, for example, sensitivity to delayed optical feedback. We study a model that consists of a hyperbolic linear system of partial…
We establish both global existence and decay properties for solutions with small data for a general class of coupled system of tensorial quasilinear hyperbolic wave equations in three space dimensions, that covers the dynamical Einstein…
A partially hyperbolic diffeomorphism $f$ has quasi-shadowing property if for any pseudo orbit ${x_k}_{k\in \mathbb{Z}}$, there is a sequence of points ${y_k}_{k\in \mathbb{Z}}$ tracing it in which $y_{k+1}$ is obtained from $f(y_k)$ by a…
The degenerate singularities of systems from one well-known multiparameter family of integrable systems of rigid body dynamics are studied. Axisymmetric Zhukovsky systems are considered, i.e. axisymmetric Euler tops after adding a constant…
The conservation laws for a class of nonlinear equations with variable coefficients on discrete and noncommutative spaces are derived. For discrete models the conserved charges are constructed explicitly. The applications of the general…
We develop a systematic procedure for constructing quantum many-body problems whose spectrum can be partially or totally computed by purely algebraic means. The exactly-solvable models include rational and hyperbolic potentials related to…
Systems of parabolic, possibly degenerate parabolic SPDEs are considered. Existence and uniqueness are established in Sobolev spaces. Similar results are obtained for a class of equations generalizing the deterministic first order symmetric…
We are concerned with global solutions of multidimensional Riemann problems for nonlinear hyperbolic systems of conservation laws, focusing on their global configurations and structures. We present some recent developments in the rigorous…
We study the time-asymptotic behavior of linear hyperbolic systems under partial dissipation which is localized in suitable subsets of the domain. More precisely, we recover the classical decay rates of partially dissipative systems…
Conditions for the existence and uniqueness of weak solutions for a class of nonlinear nonlocal degenerate parabolic equations are established. The asymptotic behaviour of the solutions as time tends to infinity are also studied. In…
A possible definition of strong/symmetric hyperbolicity for a second-order system of evolution equations is that it admits a reduction to first order which is strongly/symmetric hyperbolic. We investigate the general system that admits a…
Several interesting physical systems, such as the Lovelock extension of General Relativity in higher dimensions, classical time crystals, k-essence fields, Horndeski theories, compressible fluids, and nonlinear electrodynamics, have…
The paper deals with the decoupling problem of general quasilinear first order systems in two independent variables. We consider either the case of homogeneous and autonomous systems or the one of nonhomogeneous and/or nonautonomous…
For hyperbolic systems of conservation laws, including important physical models from continuum mechanics, the question of stability for large data solutions remains a challenging open problem. In recent work (arXiv:2507.23645) the authors…