The structural stability of Riemann solutions to the one-dimensional isentropic Chaplygin gas equations with time-dependent external force is studied. First, problem initial data two piecewise constant states solved and containing contact discontinuities delta shock waves are obtained. Then, we perturb by taking three construct global solutions. By letting perturbed parameter ɛ tend zero, show that there no mass concentration even if density depends on ɛ, which means stable under local small...

Abstract Aided by flux-approximation limits of solutions to the Suliciu relaxation system with one independent parameter, we identify phenomena concentration and cavitation. It turns out that, as flux perturbation decreases a certain critical value, any Riemann solution containing two shocks possibly one-contact-discontinuity perturbed converges its own delta-shock solution. As parameter goes zero further, limiting is just pressureless gas dynamics model; rarefaction waves...

The concentration and cavitation are fundamental physical phenomena in fluid dynamics, which can be mathematically described by delta shock waves vacuums, respectively. In this paper, we concerned with the Euler equations of compressible flow when state equation is governed extended Chaplygin gas, an important candidate for describing dark matter energy. Our main objective to apply flux-approximation method rigorously investigate formation vacuums observe phenomena. First, Riemann problem n...

The Riemann problems for a class of coupled hyperbolic systems conservation laws with source term are studied. solutions exactly include two kinds: delta-shock and vacuum solutions. In order to see more clearly the influence on solutions, generalized Rankine-Hugoniot relations delta shock waves derived in detail, position, propagation speed strength wave given. It is also shown that, as vanishes, converge corresponding ones homogeneous system, which just zero-pressure flow model contains...

Fractures phenomena can be often found in functionally graded materials (FGMs) subjected to thermal shock loadings. This paper aims develop a set of analytical-numerical methods for analyzing the mixed-mode crack problems plate (FGP). First, domain-independent interaction energy integral method is developed obtaining transient stress intensity factors (TSIFs). A perturbation adopted obtain temperature field. Then an combining method, and finite element solve present problem. Particularly,...

We demonstrate the flux-approximation problem of isothermal relativistic Euler equations describing a perfect fluid flow in special relativity. First, Riemann under flux perturbation is discussed, and four kinds solutions are obtained. Second, we rigorously prove that, as vanishes, any two-shock solution tends to delta-shock pressureless intermediate density between two shocks weighted δ-measure which forms delta shock wave. Correspondingly, two-rarefaction two-contact-discontinuity...

Article Riemann Problem for the Chaplygin Euler Equations of Compressible Fluid Flow was published on November 1, 2010 in journal International Journal Nonlinear Sciences and Numerical Simulation (volume 11, issue 11).

The Riemann problem to the Euler equations of compressible fluid flow with logarithmic pressure is first studied. Compared pressureless whose remains zero and Chaplygin gas or generalized always negative, presented in this paper can be taken any real value for positive density. But still, delta-shock wave found solution certain initial data. This peculiar phenomenon novel quite different from that isentropic same studied [Sen A, Sekhar TR. limiting behavior system equation state a source...

Article Classification and Computation of Non-resonant Double Hopf Bifurcations Solutions in Delayed van der Pol-Duffing System was published on March 1, 2005 the journal International Journal Nonlinear Sciences Numerical Simulation (volume 6, issue 1).

We investigate the interaction of delta shock waves and contact discontinuities for Chaplygin Euler equations compressible fluid flow with split functions. The perturbed Riemann problem when initial data are three piecewise constant states is constructively solved, global structure large time‐asymptotic behaviors solutions discussed case by via deriving how solution continues beyond points interaction. It shown that stable such small perturbations letting parameter ε tend to zero. Moreover,...

The last two decades have seen great progress in mathematical modeling of fluvial processes and flooding terms either approximation the physical or dealing with numerical difficulties. Yet attention to simultaneously taking advancements both aspects is rarely paid. Here a well-balanced fully coupled noncapacity model presented dam-break over erodible beds. governing equations are based on complete mass momentum conservation laws, implying interactions between flow sediment transport. A...

By introducing an isentropic Euler system with a new version of extended Chaplygin gas equation state, we study two kinds occurrence mechanism on the phenomenon concentration and formation delta shock waves in zero-exponent limit solutions to equations as exponents tend zero wholly or partly. The Riemann problem is first solved. Then, show that, both zero, that is, pressure tends constant, any two-shock-wave solution converges delta-shock zero-pressure flow system, intermediate density...

We study the interactions of delta shock waves and vacuum states for system conservation laws mass, momentum, energy in zero-pressure gas dynamics. The Riemann problems with initial data three piecewise constant are solved case by case, four different configurations solutions constructed. Furthermore, numerical simulations completely coinciding theoretical analysis shown.

Abstract By introducing a special kind of variable substitution, we skillfully solve the delta-shock and vacuum solutions to one-dimensional Eulerian droplet model. The position, propagation speed, strength delta shock wave are derived under generalised Rankine–Hugoniot relation entropy condition. Moreover, show that Riemann solution model converges corresponding pressureless Euler system as drag coefficient goes zero.

For the two-dimensional steady zero-pressure adiabatic flow, Riemann problem with delta initial data is investigated and global existence of generalized solution established in four cases. Particularly, solutions, a special type nonclassical wave called contact discontinuity Dirac functions developing both state variables found. Furthermore, we show that constructed solutions are stable by perturbation data.