Related papers: Exact solutions and conservation lawsof a one-dime…
A well-known optimal velocity (OV) model describes vehicle motion along a single lane road, which reduces to a perturbed modified Korteweg-de Vries (mKdV) equation within the unstable regime. Steady travelling wave solutions to this…
The upwind conservation element and solution element (CESE) scheme is an alternative discontinuity-capturing numerical approach to solving hyperbolic conservation laws. To evaluate the numerical properties of this spatiotemporal coupled…
In this work, a result of exponential stability is obtained for solutions of a compressible flow-structure partial differential equation (PDE) model which has recently appeared in the literature. In particular, a compressible flow PDE and…
Starting from the kinetic approach for a mixture of reacting gases whose particles interact through elastic scattering and a bimolecular reversible chemical reaction, the equations that govern the dynamics of the system are obtained by…
Center manifold analysis can be used in order to investigate the stability of the stationary solutions of various PDEs. This can be done by considering the PDE as an ODE between certain Banach spaces and linearising about the stationary…
This paper extends our earlier approach [cf. Phys. Plasmas 17, 032503 (2010), 23, 022308 (2016)] to obtaining a priori bounds on enstrophy in neutral fluids (R-Euler) and ideal magnetohydrodynamics (R-MHD). This results in a far-reaching…
In this paper, a PDE-ODE model with discontinuity in the flux as well as a flux constraint is analyzed. A modified Riemann solution is proposed and the existence of a weak solution to the Cauchy problem is rigorously investigated using the…
Blood flow in arterial systems can be described by the three-dimensional Navier-Stokes equations within a time-dependent spatial domain that accounts for the elasticity of the arterial walls. In this article blood is treated as an…
In this article we obtain exact solutions of (2+1)-dimensional Boiti-Leon-Pempinelli system of nonlinear partial differential equations which describes the evolution of horizontal velocity component of water waves propagating in two…
Some turbulent flows self-organize into large-scale structures, rather than breaking up into ever-smaller scales. Underpinning this phenomenon is the existence of two sign-definite quantities which are conserved by the dynamics.…
Ideal systems like MHD and Euler flow may develop singularities in vorticity (w = curl v). Viscosity and resistivity are dissipative regularizations. We propose a minimal, local, conservative, nonlinear, dispersive regularization of…
A new kinetic model is proposed where the equilibrium distribution with bounded support has a range of velocities about two average velocities in 1D. In 2D, the equilibrium distribution function has a range of velocities about four average…
We consider the stability of a compressible shear flow separating two streams of different speeds and temperatures. The velocity and temperature profiles in this mixing layer are hyperbolic tangents. The normal mode analysis of the flow…
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…
The problem of the flow trough a porous media is formulated in terms of a pressure equation, based on arguments of volume conservation which state the mechanical equilibrium between the solid and the fluid phases. In the resulting governing…
We present a meshfree numerical solver for scalar conservation laws in one space dimension. Points representing the solution are moved according to their characteristic velocities. Particle interaction is resolved by purely local particle…
We consider multi-dimensional extensions of Maxwell's seminal rheo-logical equation for 1D viscoelastic flows. We aim at a causal model for compressible flows, defined by semi-group solutions given initial conditions , and such that…
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…
The contribution of the "rapid" part of the pressure diffusion to the turbulent kinetic energy balance is analyzed, and a new model to describe its effect is suggested. A new transport equation for the turbulent kinetic energy is derived.…
We find a representation of smooth solutions to the Cauchy problem for a scalar multidimensional conservation law as small diffusion limit of a stochastic perturbation along characteristics. It helps, in particular, to study the process of…