摘要:

We show here that the weak solutions of the quasilinear hyperbolic systemconverge, as ∈ tends to zero, to the solution of the reduced problemso that υ satisfies the nonlinear parabolic equationThe limiting procedure is carried out by using the theory of compensated compactness. Finally we obtain the existence of Lyapounov functionals for the limit parabolic equation as weak limit of the convex entropies as ∈ tends to zero for the corresponding hyperbolic system.

ISSN:0360-5302    

DOI:10.1080/03605309608821172

出版商:Marcel Dekker, Inc.    

年代:1996

数据来源: Taylor

摘要:

*Department of Mathematics, E.T.M.A., University of Toulon end of Var, La Garde,France†Department of Mathematics, E.T.M.A., University of Toulon end of Var, La Garde,France

ISSN:0360-5302    

DOI:10.1080/03605309608821173

出版商:Marcel Dekker, Inc.    

年代:1996

数据来源: Taylor

ISSN:0360-5302    

DOI:10.1080/03605309608821174

出版商:Marcel Dekker, Inc.    

年代:1996

数据来源: Taylor

摘要:

We present global existence theorem for semilinear schrödinger equations. In general, Schrödinger-type equations do not admit the classical energy estimates. To avoid this difficulty, we use S. Doi's method for linear Schrödinger-type equations. Combining his method and Lp-Lqestimates, we prove the global existence of solutions with small initial data.

ISSN:0360-5302    

DOI:10.1080/03605309608821175

出版商:Marcel Dekker, Inc.    

年代:1996

数据来源: Taylor

摘要:

We prove local existence and uniqueness of low regularity solutions to semi-linear systems. The Smoothness of our solutions is below the classical level. The main lemma is anL2estimate for products of solutions of linear equations inspried by earlier work by Strichartz, Klainerman and Machedon.

ISSN:0360-5302    

DOI:10.1080/03605309608821176

出版商:Marcel Dekker, Inc.    

年代:1996

数据来源: Taylor

摘要:

*Supported in part by NSF grant DMS-9305044.†Current address: IMA. University of Minnesota, Minneapolis, MN 56455

ISSN:0360-5302    

DOI:10.1080/03605309608821180

出版商:Marcel Dekker, Inc.    

年代:1996

数据来源: Taylor

摘要:

We give a solution of below-up problem for equation, with data close to constans, in any number of spce dimensions: there exists a blow-up surface, near which the solution has logarithmic behavior; its smoothness is estimated in terms of the smoothness of the data. More precisely, we prove that for any solution ofwith Cauchy data ont = 1close to (ln2, -2) insis a large enough integer, must blow-up on a space like hypersurface defined by an equationt = ψ(x)with. Furthermore, the solution has an asymptotic expansionwhereT = t - ψ(x), valid upto orders - 151 - 10[n/2]. Logarithmic terms are absent if and only if the blow-up surface has vanishing scalar curvature. The blow-up time can be identified with the infimum of the function ψ. Although attention is focused on one equation, the strategy is quite general; it consists in applying the Nash-Moser IFT to a map “singularity data ” to Cauchy data.

ISSN:0360-5302    

DOI:10.1080/03605309608821177

出版商:Marcel Dekker, Inc.    

年代:1996

数据来源: Taylor

ISSN:0360-5302    

DOI:10.1080/03605309608821178

出版商:Marcel Dekker, Inc.    

年代:1996

数据来源: Taylor

摘要:

We construct self-similar solutions for three-dimensional incompressible Navier-Stokes equations, providing some examples of functional spaces where this can be done. We apply our results to a Particular case of L2initial data.

ISSN:0360-5302    

DOI:10.1080/03605309608821179

出版商:Marcel Dekker, Inc.    

年代:1996

数据来源: Taylor

ISSN:0360-5302    

DOI:10.1080/03605309608821181

出版商:Marcel Dekker, Inc.    

年代:1996

数据来源: Taylor