convergence of the viscosity method for isentropic gas dynamics a convergence theorem for the method of artificial viscosity applied to the isentropic equations of gas dynamics is established convergence of a subsequence in the strong topology is proved without uniform estimates on the derivatives using the theory of compensated compactness and an analysis of progressing entropy waves

local existence of weak solutions to the quasi linear wave equation for large initial values on considere le probleme aux valeurs initiales hyperbolique quasilineaire suivant u t f u x x r t 0 u x o u x avec u u 1 u 2 r r 0 r 2 u u u 2 r r 2 f u u 2 u 1

global stability of rarefaction wave to the 1 d piston problem for the compressible full euler equations abstract in this paper we study the 1 d piston problem for compressible full euler equations under the assumptions that the total variation of the initial data and the perturbation of the piston velocity are sufficiently small by a modified wave front tracking method we establish the global existence of entropy solutions including a strong rarefaction wave without restriction on the strength moreover we establish the asymptotic behavior of the solutions as t

steady supersonic flow past an almost straight wedge with large vertex angle abstract this paper studies the problem on the steady supersonic flow at the constant speed past an almost straight wedge with a piecewise smooth boundary it is well known that if each vertex angle of the straight wedge is less than an extreme angle determined by the shock polar the shock wave is attached to the tip of the wedge and constant states on both side of the shock are supersonic this paper is devoted to generalizing this result under the hypotheses that each vertex angle is less than the extreme angle and the total variation of tangent angle along each edge is sufficiently small a sequence of approximate solutions constructed by a modified glimm scheme is proved to be convergent to a global weak solution of the steady problem a sequence of the corresponding approximate leading shock fronts issuing from the tip is shown to be convergent to the leading shock front of the obtained solution the regularity of the leading shock front is established and the asymptotic behaviour of the obtained solution at infinity is also studied

solutions in the large for the nonlinear hyperbolic conservation laws of gas dynamics the constraints under which a gas at a certain state will evolve can be given by three partial differential equations which express the conservation of momentum mass and energy in these equations a particular gas is defined by specifying the constitutive relation e e u s where e specific internal energy v specific volume and s specific entropy the energy function e in u s r describes a polytropic gas for the exponent y 1 and for this choice of e v s global weak solutions for bounded measurable data having finite total variation were given by nishida in lo here the following general existence theorem is obtained let e v s be any smooth one parameter family of energy functions such that at e 0 the energy is given by e v s in v s r it is proven that there exists a constant c independent of e such that if e total variation of the initial data c then there exists a global weak solution to the equations since any energy function can be connected to e v s by a smooth parameterization our results give an existence theorem for all the conservation laws of gas dynamics as a corollary we obtain an existence theorem of liu indiana univ math j 26 no 1 1977 for polytropic gases the main point in this argument is that the nonlinear functional used to make the glimm scheme converge depends only on properties of the equations at e 0 for general n x n systems of conservation laws this technique provides an alternate proof for the interaction estimates in glimm s 1965 paper the new result here is that certain interaction differences are bounded by e as well as by the approaching waves

sufficient conditions for local existence via glimm s scheme for large bv data abstract using glimm s scheme sufficient conditions are derived for the global existence of a weak solution to a strictly hyperbolic genuinely nonlinear system of partial differential equations in one space dimension when the initial data is a small bv perturbation of a solvable riemann problem by using the finite propagation speed of the system this yields a local existence theorem for arbitrary bv initial data that satisfies the above mentioned conditions at all large jumps the case of linearly degenerate fields is also treated and the results are applied to the p system and to the 1 d nonisentropic gas law euler equations

solutions a variations bornees pour certains systemes hyperboliques de lois de conservation abstract blake temple trans amer math soc 280 1983 781 795 has described the hyperbolic systems of two conservation laws whose shock and rarefaction curves coincide in this note we prove the global existence of weak solutions for such systems with any bounded variation initial condition the proof is based upon standard numerical schemes as well as upon parabolic regularization the key is that the total variation of the riemann invariants is decreasing in time at least in the case of the initial condition with compact support we prove by using the glimm scheme that the system is decoupling in two conservation laws in one unknown in finite time

stability theorem and truncation error analysis for the glimm scheme and for a front tracking method for flows with strong discontinuities typical nonlinear wave interaction problems involve strong waves moving through a background of weak disturbance previous existence theorems and error analysis for computations are usually restricted to more idealized situations such as small data or single equations we consider here the problem of a single strong discontinuity interacting with a weak background for general hyperbolic systems of conservation laws we obtain the stability consistency theorems and upper bounds of the truncation errors for the glimm scheme and for a front tracking method the major error in the glimm scheme is the error generated by the strong discontinuity this error is reduced when a front tracking method is applied to follow the location of the strong discontinuity this demonstrates an advantage of front tracking methods in one space dimension

almost global existence of classical discontinuous solutions to genuinely nonlinear hyperbolic systems of conservation laws with small bv initial data abstract in the present paper the author investigates the initial problem for genuinely nonlinear quasilinear hyperbolic systems of conservation laws under small bv perturbations of the riemann initial data where the perturbations are in bv but they are assumed to be c 1 smooth with bounded and possibly large c 1 norms combining the techniques employed by li and kong with the modified glimm s functional the author obtains the almost global existence and lifespan of classical discontinuous solutions to the above problem this result is also applied to the system of one dimensional isentropic flow

a convergent series expansion for hyperbolic systems of conservation laws the discontinuities piecewise analytic initial value problem for a wide class of conservation laws is considered which includes the full three dimensional euler equations the initial interaction at an arbitrary curved surface is resolved in time by a convergent series among other features the solution exhibits shock contact and expansion waves as well as sound waves propagating on characteristic surfaces the expansion waves correspond to he one dimensional rarefactions but have a more complicated structure the sound waves are generated in place of zero strength shocks and they are caused by mismatches in derivatives

the generalized nonlinear initial boundary riemann problem for linearly degenerate quasilinear hyperbolic systems of conservation laws abstract this work is a continuation of our previous work in the present paper we study the generalized nonlinear initial boundary riemann problem with small bv data for linearly degenerate quasilinear hyperbolic systems of conservation laws with nonlinear boundary conditions in a half space t x t 0 x 0 we prove the global existence and uniqueness of piecewise c 1 solution containing only contact discontinuities to a class of the generalized nonlinear initial boundary riemann problem which can be regarded as a small bv perturbation of the corresponding nonlinear initial boundary riemann problem for general n n linearly degenerate quasilinear hyperbolic system of conservation laws moreover this solution has a global structure similar to the one of the self similar solution u u x t to the corresponding nonlinear initial boundary riemann problem some applications to quasilinear hyperbolic systems of conservation laws arising in the string theory and high energy physics are also given

on the controllability of the non isentropic 1 d euler equation in this paper we examine the question of the boundary controllability of the one dimensional non isentropic euler equation for compressible polytropic gas in the context of weak entropy solutions we consider the system in eulerian coordinates and the one in lagrangian coordinates we obtain for both systems a result of controllability toward constant states with the limitation gamma frac 5 3 on the adiabatic constant for the lagrangian system the solutions that we obtain remain of small total variation in space if the initial condition is itself of sufficiently small total variation

conditional spectral analysis of replicated multiple time series with application to nocturnal physiology abstractthis article considers the problem of analyzing associations between power spectra of multiple time series and cross sectional outcomes when data are observed from multiple subjects the motivating application comes from sleep medicine where researchers are able to noninvasively record physiological time series signals during sleep the frequency patterns of these signals which can be quantified through the power spectrum contain interpretable information about biological processes an important problem in sleep research is drawing connections between power spectra of time series signals and clinical characteristics these connections are key to understanding biological pathways through which sleep affects and can be treated to improve health such analyses are challenging as they must overcome the complicated structure of a power spectrum from multiple time series as a complex positive definite matrix valued function this article proposes a new approach to such analyses based on a tensor pr

propagating phase boundaries formulation of the problem and existence via the glimm method this paper treats the hyperbolic elliptic system of two conservation laws which describes the dynamics of an elastic material having a non monotone strain stress function followingabeyaratne knowles we propose a notion of admissible weak solution for this system in the class of functions of bounded variation the formulation includes an entropy inequality a kinetic relation imposed along any subsonic phase boundary and an initiation criterion for the appearance of new phase boundaries we prove thel1 continuous dependence of the solution to the riemann problem our main result yields the existence and the stability of propagating phase boundaries the proofs are based onglimm s scheme and in particular on the techniques ofglimm andlax in order to deal with the kinetic relation we prove a result of pointwise convergence of the phase boundary

saddle point reduction method for some non autonomous second order systems abstract the purpose of this paper is to study the existence of solutions with saddle point character for non autonomous second order systems u t f t u t a e t 0 t u 0 u t u 0 u t 0 some new solvability conditions are obtained

steady supersonic flow past a curved cone abstract this paper studies the steady supersonic flow past a lipschitz curved cone under the assumptions that the cone has an opening angle less than a critical value and has sufficiently small total variation of the tangent of the perturbation and that the mach number of incoming flow is sufficiently large the global weak solution is constructed via glimm scheme for 1 3

lifespan of classical discontinuous solutions to general quasilinear hyperbolic systems of conservation laws with small bv initial data rarefaction waves abstract in the present paper the author investigates the global structure stability of riemann solutions for general quasilinear hyperbolic systems of conservation laws under small bv perturbations of the initial data where the riemann solution contains rarefaction waves while the perturbations are in bv but they are assumed to be c 1 smooth with bounded and possibly large c 1 norms combining the techniques employed by li kong with the modified glimm s functional the author obtains a lower bound of the lifespan of the piecewise c 1 solution to a class of generalized riemann problems which can be regarded as a small bv perturbation of the corresponding riemann problem this result is also applied to the system of traffic flow on a road network using the aw rascle model