摘要:

AbstractIn this paper, we prove that the functional which takes a closed Lavrentiev curve to the corresponding Riemann mapping is locally Lipl on the set Ω of all closed Lavrentiev curves. This set is a subset of BMO(T). It is, however, not open in BMO(T). We also prove that the previous functional is analytic for certain classes of closed Lavrentiev curves, including the class of curves which have some symmetry with respect to the unit circle. These classes of curves are submanifolds of BMO(T). Finally, we consider the functional which takes a Lavrentiev curve (closed or not) inn‐dimensional Euclidean space to the corresponding minimal surface, and we study the differentiability and analyticity of this functional on certain function spaces. © 1993 John Wiley&Sons,

ISSN:0010-3640    

DOI:10.1002/cpa.3160461002

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

年代:1993

数据来源: WILEY

摘要:

AbstractDifference approximations of hyperbolic partial differential equations with highly oscillatory coefficients and initial values are studied. Analysis of strong and weak convergence is carried out in the practically interesting case when the discretization step sizes are essentially independent of the oscillatory wave lengths. © 1993 John Wiley&Sons, Inc

ISSN:0010-3640    

DOI:10.1002/cpa.3160461003

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

年代:1993

数据来源: WILEY

摘要:

AbstractWe consider solutions of the singular diffusion equationt, = (um−1ux)x,m≦ 0, associated with the flux boundary condition limx→−∞(um−1ux)x= λ>0. The evolutions defined by this problem depend on bothmand λ. We prove existence and stability of traveling wave solutions, parameterized by λ. Each traveling wave is stable in its appropriate evolution. These traveling waves are inL1for −1

ISSN:0010-3640    

DOI:10.1002/cpa.3160461004

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

年代:1993

数据来源: WILEY

摘要:

AbstractAxisymmetric vortex rings with swirl in an inviscid incompressible fluid are considered and it is demonstrated how the geometrical optics method can be used for investigating their stability. The evolution of rapidly oscillating initial data is studied and it is shown that the corresponding rings are unstable if the transport equations associated with the wave which is advected by the flow have unbounded solutions. It is shown that unbounded solutions grow either exponentially or algebraically. By means of the analysis of the corresponding transport equations effective stability conditions for general vortex rings with swirl are obtained. © 1993 John Wiley&Sons, Inc

ISSN:0010-3640    

DOI:10.1002/cpa.3160461005

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.3160461001

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

年代:1993

数据来源: WILEY