摘要:

AbstractWe study the limiting behavior of systems of hyperbolic conservation laws with stiff relaxation terms. Reduced systems, inviscid and viscous local conservation laws, and weakly nonlinear limits are derived through asymptotic expansions. An entropy condition is introduced forN×Nsystems that ensures the hyperbolicity of the reduced inviscid system. The resulting characteristic speeds are shown to be interlaced with those of the original system. Moreover, the first correction to the reduced system is shown to be dissipative. A partial converse is proved for 2 × 2 systems. This structure is then applied to study the convergence to the reduced dynamics for the 2 × 2 case. © 1994 John Wiley&Sons,

ISSN:0010-3640    

DOI:10.1002/cpa.3160470602

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1994

数据来源: WILEY

摘要:

AbstractI consider the nonlinear stability of plane wave solutions to a Ginzburg‐Landau equation with additional fifth‐order terms and cubic terms containing spatial derivatives. I show that, under the constraint that the diffusion coefficient be real, these waves are stable. Furthermore, it is shown that the radial component of the perturbation decays at a faster rate than the phase component of the perturbation ast→ ∞. The result is also applicable to the classical Ginzburg‐Landau equation. © 1994 John Wiley

ISSN:0010-3640    

DOI:10.1002/cpa.3160470603

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1994

数据来源: WILEY

摘要:

AbstractLet be a hypoelliptic diffusion operator on a compact manifoldM. Given an a priori smooth reference measure λ onM, we can then rewriteLas the sum of a λ‐symmetric partL0and a first‐order drift partY. The paper investigates the effect of the driftYon the Donsker‐Varadhan rate function corresponding to the large deviations of the empirical measure of the diffusion. WhenYis in the linear span of the first and second‐order Lie brackets of the Xi's, we derive an affine bound relating the rate functions associated with L and L0. As soon as one point exists whereYis not in the linear span of the first and second‐order Lie brackets of the Xi's, we show that such an affine bound is impossible. © 1994 John Wil

ISSN:0010-3640    

DOI:10.1002/cpa.3160470604

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1994

数据来源: WILEY

ISSN:0010-3640    

DOI:10.1002/cpa.3160470605

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1994

数据来源: WILEY

摘要:

AbstractWe present a general method for studying long‐time asymptotics of nonlinear parabolic partial differential equations. The method does not rely on a priori estimates such as the maximum principle. It applies to systems of coupled equations, to boundary conditions at infinity creating a front, and to higher (possibly fractional) differential linear terms. We present in detail the analysis for nonlinear diffusion‐type equations with initial data falling off at infinity and also for data interpolating between two different stationary solutions at infinity. In an accompanying paper, [5], the method is applied to systems of equations where some variables are “slaved,” such as the complex Ginzburg‐Landau equation. © 1994 John Wiley

ISSN:0010-3640    

DOI:10.1002/cpa.3160470606

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1994

数据来源: WILEY

ISSN:0010-3640    

DOI:10.1002/cpa.3160470601

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1994

数据来源: WILEY