Related papers: Evolution of interface singularities in shallow wa…
In this article we investigate a system of geometric evolution equations describing a curvature driven motion of a family of 3D curves in the normal and binormal directions. Evolving curves may be subject of mutual interactions having both…
We study the long time evolution of internal waves in two dimensional subcritical channels with flat horizontal ends. We show the leading profiles of solutions are the outgoing solutions to the stationary equations. This is done by showing…
We study the propagation of singularities in solutions of linear convection equations with spatially heterogeneous nonlocal interactions. A spatially varying nonlocal horizon parameter is adopted in the model, which measures the range of…
The process of interaction between nonlinear waves on a free surface of a nonconducting fluid in a strong tangential electric field is simulated numerically (effects of the force of gravity and capillarity are neglected). It is shown that…
Shallow free surface flows are often characterized by both subdomains that require high modeling complexity and subdomains that can be sufficiently accurately modeled with low modeling complexity. Moreover, these subdomains may change in…
The propagation of nonlinear waves in one dimensional space, unsteady and compressible flow in Darcy-type porous media is analyzed. It is assumed that the weak discontinuity propagate long the characteristic path using the characteristics…
Many physical situations are characterized by interfaces with a non trivial shape so that relevant geometric features, such as interfacial area, curvature or unit normal vector, can be used as main indicators of the topology of the…
This paper is an attempt to classify finite-time singularities of PDEs. Most of the problems considered describe free-surface flows, which are easily observed experimentally. We consider problems where the singularity occurs at a point, and…
We consider models of relativistic matter containing sharp interfaces across which the matter model changes. These models will be relevant for neutron stars with crusts, phase transitions, or for viscous boundaries where the length scale is…
In an earlier work we have shown the global (for all initial data and all time) well-posedness of strong solutions to the three-dimensional viscous primitive equations of large scale oceanic and atmospheric dynamics. In this paper we show…
Nonlinear waves are a robust phenomenon observed in complex systems ranging from mechanics to ecology. Fronts are fundamental due to their robustness against perturbations and capacity to propagate one state over another. Controlling and…
This paper investigates solitary water waves propagating along the surface of a two-dimensional dielectric fluid with constant vorticity in the presence of an external electric field. We formulate the system as a nonlinear free boundary…
In this work, we derive reduced interface models for hydroelastic water waves coupled to a nonlinear viscoelastic plate. In a weakly nonlinear small-steepness regime we obtain bidirectional nonlocal evolution equations capturing the…
This paper provides a theoretical foundation for some common formulations of inverse problems in wave propagation, based on hyperbolic systems of linear integro-differential equations with bounded and measurable coefficients. The…
A series of laboratory experiments has been carried out in a thermally driven rotating annulus to study the onset of baroclinic instability, using horizontal and uniformly sloping bottom topographies. Different wave flow regimes have been…
We study the free boundary evolution between two irrotational, incompressible and inviscid fluids in 2-D without surface tension. We prove local-existence in Sobolev spaces when, initially, the difference of the gradients of the pressure in…
In this letter we review the separate universe approach for cosmological perturbations and point out that it is essentially the lowest order approximation to a gradient expansion. Using this approach, one can study the nonlinear evolution…
We investigate the evolution of interfaces among phases of the interstellar medium with different temperature. It is found that, for some initial conditions, the dynamical effects related to conductive fronts are very important even if…
We study the mass-conserved reaction-diffusion system known as the wave-pinning model, which serves as a minimal framework for describing cell polarity. In this model, the interplay between reaction kinetics and slow diffusion forms a sharp…
We consider a non-linear system modelling the dynamics of a linearly elastic body immersed in an incompressible viscous fluid, without damping on the elastic part. We prove local existence of strong solutions and global existence and…