摘要:

AbstractMulti‐valued solutions are constructed for 2 × 2 first‐order systems using a generalization of the hodograph transformation. The solution is found as a complex analytic function on a complex Riemann surface for which the branch points move as part of the solution. The branch point singularities are envelopes for the characteristics and thus move at the characteristic speeds. We perform an analysis of stability of these singularities with respect to perturbations of the initial data. The generic singularity types are folds, cusps, and nondegenerate umbilic points with non‐zero 3‐jet. An isolated singularity is generically a square root branch point corresponding to a fold. Two types of collisions between singularities are generic: At a “tangential” collision between two singularities moving at the same characteristic speed, a cube root branch point is formed, corresponding to a cusp. A “non‐tangential” collision, between two square root branch points moving at different characteristic speeds, remains a square root branch point at the collision and corresponds to a nondegenerate umbilic point. These results are also valid for a diagonalizablen‐th order system for which there are exactly two speeds. © 1993

ISSN:0010-3640    

DOI:10.1002/cpa.3160460402

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

年代:1993

数据来源: WILEY

ISSN:0010-3640    

DOI:10.1002/cpa.3160460403

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

年代:1993

数据来源: WILEY

摘要:

AbstractTravelling waves of a viscous conservation law (so‐called viscous profiles) are shown to be stable in polynomialy weightedL∞spaces. There is no assumption of convexity on the nonlinear term and thus earlier results of Il'in and Oleǐnik, Sattinger, and Kawashima and Matsumura are generalized. The method uses the semigroup of the linearized equation with solutions of the full problem expressed by the variation of constants formula. Estimates are derived for the semigroup through a new technique for estimating the resolvent. © 1993 John Wiley&Sons

ISSN:0010-3640    

DOI:10.1002/cpa.3160460404

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

年代:1993

数据来源: WILEY

ISSN:0010-3640    

DOI:10.1002/cpa.3160460405

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

年代:1993

数据来源: WILEY

ISSN:0010-3640    

DOI:10.1002/cpa.3160460401

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

年代:1993

数据来源: WILEY