相关论文: Sharp pointwise bounds for perturbed viscous shock…
In this paper we propose the first framework to study Burgers' equation featuring critical fast diffusion in form of $u_t+f(u)_x = (\ln u)_{xx}$. The solution possesses a strong singularity when $u=0$ hence bringing technical challenges.…
This paper is concerned with nonlinear stability of viscous contact discontinuity to a free boundary problem for the one-dimensional full compressible Navier-Stokes equations in half space $[0,\infty)$. For the case when the local stability…
We are able to detect the details of spatial optical collisionless wave-breaking through the high aperture imaging of a beam suffering shock in a fluorescent nonlinear nonlocal thermal medium. This allows us to directly measure how…
The idea of using fast sweeping methods for solving stationary systems of conservation laws has previously been proposed for efficiently computing solutions with sharp shocks. We further develop these methods to allow for a more challenging…
We consider a class of blow-up solutions for perturbed nonlinear heat equations involving gradient terms. We first prove the single point blow-up property for this equation and determine its final blow-up profile. We also give a sharper…
We consider the free boundary problem for a layer of viscous, incompressible fluid in a uniform gravitational field, lying above a rigid bottom and below the atmosphere. For the "semi-small" initial data, we prove the zero surface tension…
An analytical method within the frame of linear stability theory is presented for the normal field instability in magnetic fluids. It allows to calculate the maximal growth rate and the corresponding wave number for any combination of…
By reduction to a generalized Sturm Liouville problem, we establish spectral stability of hydraulic shock profiles of the Saint-Venant equations for inclined shallow-water flow, over the full parameter range of their existence, for both…
It is well known that the standard transport equations violate causality when gradients are large or when temporal variations are rapid. We derive a modified set of transport equations that satisfy causality. These equations are obtained…
Sharp temporal decay estimates are established for the gradient and time derivative of solutions to a viscous Hamilton-Jacobi equation as well the associated Hamilton-Jacobi equation. Special care is given to the dependence of the estimates…
We describe recent analytical and numerical results on stability and behavior of viscous and inviscid detonation waves obtained by dynamical systems/Evans function techniques like those used to study shock and reaction diffusion waves. In…
Pseudospectral schemes are a class of numerical methods capable of solving smooth problems with high accuracy thanks to their exponential convergence to the true solution. When applied to discontinuous problems, such as fluid shocks and…
In this paper, we propose the uncertain volatility models with stochastic bounds. Like the regular uncertain volatility models, we know only that the true model lies in a family of progressively measurable and bounded processes, but instead…
To investigate the formation and the propagation of relativistic shock waves in viscous gluon matter we solve the relativistic Riemann problem using a microscopic parton cascade. We demonstrate the transition from ideal to viscous shock…
This paper is concerned with the asymptotic stability of a composite wave of two viscous shocks under spatially periodic perturbations for the 1-D full compressible Navier-Stokes equations. It is proved that as time increases, the solution…
We derive analytically some general features of the power-law sensitivity curve. They include an exact parametric equation, a formula for the peak sensitivity and a proof of convexity in log-log plot. A few conceptual points are also…
This paper studies the behavior of singularly perturbed nonlinear differential equations with boundary-layer solutions that do not necessarily converge to an equilibrium. Using the average of the fast variable and assuming the boundary…
We consider a class of linear second order differential equations with damping and external force. We investigate the link between a uniform bound on the forcing term and the corresponding ultimate bound on the velocity of solutions, and we…
Dispersive shock waves are fascinating phenomena occurring when nonlinearity overwhelms linear effects, such as dispersion and diffraction. Many features of shock waves are still under investigation, as the interplay with noninstantaneity…
The condition of linear instability for a converging cylindrical strong shock wave (SW) in an arbitrary viscous medium is obtained in the limit of a large stationary SW radius, when it is possible to consider the same Rankine-Hugoniot jump…