We consider the weakly dissipative and weakly dispersive Burgers-Hopf-Korteweg-de-Vries equation with the diffusion coefficient ε and the dispersion rate δ in the range δ/ε → 0. We study the travelling wave connecting u(−∞) = 1 to u(+∞) = 0 and show that it converges strongly to the entropic shock profile as ε, δ → 0. Key-words Travelling waves, moderate dispersion, Korteweg de Vries equation, ...

As noted by the second author in the context of unstable two-phase porous medium flow, entropy solutions of Burgers’ equation can be recovered from a minimizing movement scheme involving the Wasserstein metric in the limit of vanishing time step size [4]. In this paper, we give a simpler proof by verifying that the anti-derivative is a viscosity solution of the associated Hamilton Jacobi equati...

We describe a kinetic theory for shock clustering in scalar conservation laws with random initial data. Our main discovery is that for a natural class of random data the shock clustering is described by a completely integrable Hamiltonian system. Thus, the problem is in a precise sense exactly solvable. Our results have implications in other areas: mathematical physics (limits of shell models o...

Burgers' equation is a well-studied model in applied mathematics with connections to the Navier-Stokes equations one spatial direction and traffic flow, for example. Following on from previous work, we analyse solutions complex plane, concentrating dynamics of singularities their relationship solution real line. For an initial condition simple pole each upper- lower-half planes, apply formal as...

Abstract Computational fluid dynamics (CFD) simulations are a vital part of the design process in aerospace industry. Although reliable CFD results can be obtained with turbulence models, direct numerical simulation complex bodies three spatial dimensions (3D) is impracticable due to massive amount computational elements. For instance, 3D turbulent boundary-layer over wing commercial jetliner t...

The SBV regularity of weak entropy solutions to the Burgers-Poisson equation for initial data in L 1 ( R ) is considered. We show that derivative a solution consists only absolutely continuous part and jump part.