1,720,975 research outputs found
On The Well-posedness Of Higher Order Viscous Burgers' Equations
No full textWe consider higher order viscous Burgers' equations with generalized nonlinearity and study the associated initial value problems for given data in the L2-based Sobolev spaces. We introduce appropriate time weighted spaces to derive multilinear estimates and use them in the contraction mapping principle argument to prove local well-posedness for data with Sobolev regularity below L2. We also prove ill-posedness for this type of models and show that the local well-posedness results are sharp in some particular cases viz., when the orders of dissipation p, and nonlinearity k+1, satisfy a relation p=2k+1. © 2014 Elsevier Inc.4171122Birnir, B., Kenig, C.E., Ponce, G., Svanstedt, N., Vega, L., On the ill-posedness of the IVP for the generalized Korteweg-de Vries and nonlinear Schrödinger equations (1996) J. Lond. Math. Soc., 53, pp. 551-559Bourgain, J., Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. II. The KdV-equation (1993) Geom. Funct. Anal., 3, pp. 209-262Bourgain, J., Periodic Korteweg de Vries equation with measures as initial data (1997) Selecta Math. (N.S.), 3, pp. 115-159Carvajal, X., Panthee, M., Well-posedness of KdV type equations (2012) Electron. J. Differential Equations, 2012 (40), pp. 1-15Carvajal, X., Panthee, M., Sharp local well-posedness of KdV type equations with dissipative perturbations, , arxiv:1304.6640v1Carvajal, X., Panthee, M., A note on local well-posedness of generalized KdV type equations with dissipative perturbations, , arxiv:1305.0511Carvajal, X., Scialom, M., On the well-posedness for the generalized Ostrovsky, Stepanyams and Tsimring equation (2005) Nonlinear Anal., 62 (2), pp. 1277-1287Chen, W., Li, J., On the low regularity of the modified Korteweg-de Vries equation with a dissipative term (2007) J. Differential Equations, 240, pp. 125-144Christ, M., Colliander, J., Tao, T., Asymptotics, frequency modulation, and low regularity illposedness for canonical defocusing equations (2003) Amer. J. Math., 125, pp. 1235-1293Colliander, J., Keel, M., Staffilani, G., Takaoka, H., Tao, T., Global well-posedness for KdV in Sobolev spaces of negative index (2001) Electron. J. Differential Equations, 2001 (26), p. 7Colliander, J., Keel, M., Staffilani, G., Takaoka, H., Tao, T., Sharp global well-posedness for KdV and modified KdV on R and T (2003) J. Amer. Math. Soc., 16, pp. 705-749Dix, D.B., Nonuniqueness and uniqueness in the initial value problem for Burgers' equation (1996) SIAM J. Math. Anal., 27, pp. 708-724Grünrock, A., A bilinear Airy-estimate with application to gKdV-3 (2005) Differential Integral Equations, 18 (12), pp. 1333-1339Han, J., Peng, L., The well-posedness of the dissipative Korteweg-de Vries equations with low regularity data (2008) Nonlinear Anal., 69, pp. 171-188Kenig, C.E., Ponce, G., Vega, L., Well-posedness and scattering results for the generalized Korteweg-de Vries equation via the contraction principle (1993) Comm. Pure Appl. Math., 46 (4), pp. 527-620Kenig, C.E., Ponce, G., Vega, L., A bilinear estimate with applications to the KdV equation (1996) J. Amer. Math. Soc., 9 (2), pp. 573-603Kenig, C.E., Ponce, G., Vega, L., On the ill-posedness of some canonical dispersive equations (2001) Duke Math. J., 106 (3), pp. 617-633Molinet, L., Ribaud, F., On the low regularity of the Korteweg-de Vries-Burgers equation (2002) Int. Math. Res. Not. IMRN, 37, pp. 1979-2005Molinet, L., Ribaud, F., Youssfi, A., Ill-posedness issue for a class of parabolic equations (2002) Proc. Roy. Soc. Edinburgh Sect. A, 132, pp. 1407-1416Molinet, L., Saut, J.-C., Tzvetkov, N., Ill-posedness issues for the Benjamin-Ono and related equations (2001) SIAM J. Math. Anal., 4, pp. 982-988Otani, M., Well-posedness of the generalized Benjamin-Ono-Burgers equations in Sobolev spaces of negative order (2006) Osaka J. Math., 43, pp. 935-965Tzvetkov, N., Remark on the local ill-posedness for KdV equation (1999) C. R. Math. Acad. Sci. Paris, 329, pp. 1043-104
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
The effect of higher-order dissipation on solutions of the generalized Korteweg-de Vries equation
No full textThis paper is concerned with the generalized Korteweg-de Vries equation partial derivative(t)u + partial derivative(x)u + u(p)partial derivative(x)u + partial derivative(3)(x)u = 0 in the supercritical case p > 4. For such values of p, it is expected that large, smooth initial data can lead to locally smooth solutions that blow up in finite time. The question raised here is whether or not the addition of a suitable dissipative term could mitigate this putative blowup. The dissipative addition considered is of the form (-1)(m)nu partial derivative(2m)(x)u where nu > 0 and m is a non-negative integer. It turns out that for m >= 2, there are values of p > 4 for which global well-posedness obtains for arbitrarily large initial data for any nu > 0, no matter how small. In general, it is shown that for any value of p and initial data u0 whose norm is bounded by M, say, there is a nu 0 depending on M such that if nu > nu 0, then the solution emanating from u0 is global. However, if p > 4m - 2, numerical simulations show that solutions can still blow up even in the presence of dissipation if nu is not large enough.
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Get PDFWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Dispelling the Myths Behind First-author Citation Counts
Get PDFWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
On Uniqueness Of Solution For A Nonlinear Schrödinger-airy Equation
No full textWe prove that a sufficiently smooth solution to the initial value problem associated to the equation∂tu+iα∂x2u+β∂x3u+iγ |u|2u+δ|u|2∂xu+εu2∂xū=0,x,t∈R,is uniquely determined by its values in the semi-line at two different instants of time. © 2005 Elsevier Ltd. All rights reserved.641146158Bourgain, J., On the compactness of the support of solutions of dispersive equations (1997) Int. Math. Res. Notices, 9, pp. 437-447Carvajal, X., (2002), Ph.D. Thesis, IMPA, Rio de Janeiro, BrazilCarvajal, X., Linares, F., (2003) Some Properties for a Higher Order Nonlinear Schrödinger Equation, , PreprintCarvajal, X., Linares, F., A higher order nonlinear Schrödinger equation with variable coefficients (2003) Diff. Int. Equations, 16, pp. 1111-1130Carvajal, X., Panthee, M., Unique continuation property for a higher order nonlinear Schrödinger equation (2005) J. Math. Anal. Appl., 303 (1), pp. 188-207Hasegawa, A., Kodama, Y., Nonlinear pulse propagation in a monomode dielectric guide (1987) IEEE J. Quantum Electron., 23 (5), pp. 510-524Iório Jr., R.J., (2001) Unique Continuation Principles for the Benzamin-Ono Equation, , Preprint, IMPAIório Jr., R.J., (2002) Unique Continuation Principles for Some Equations of Benzamin-Ono Type, , Preprint, IMPAIsakov, V., Carleman type estimates in an anisotropic case and applications (1993) J. Diff. Equations, 105, pp. 217-238Kenig, C.E., Ponce, G., Vega, L., On the support of solutions to the generalized KdV equation (2002) Ann. Inst. H. Poincaré Anal. Non Linéaire, 19 (2), pp. 191-208Kenig, C.E., Ponce, G., Vega, L., On the unique continuation of solutions to the generalized KdV equation (2003) Math. Res. Lett., 10 (5-6), pp. 833-846Kenig, C.E., Ponce, G., Vega, L., On unique continuation for nonlinear Schrödinger equation (2003) Commun. Pure Appl. Math., 56, pp. 1247-1262Kenig, C.E., Ruiz, A., Sogge, C., Uniform Sobolev inequalities and unique continuation for second order constant coefficient differential operators (1987) Duke Math. J., 55, pp. 329-347Kodama, Y., Optical solitons in a monomode fiber (1985) J. Statist. Phys., 39 (56), pp. 597-614Laurey, C., The Cauchy problem for a third order nonlinear Schrödinger equation (1997) Nonlinear Anal.Theory, Methods and Appl., 29, pp. 121-158Mizohata, S., Unicité du prolongement des solutions pour quelques operateurs differentials paraboliques (1958) Mem. Coll. Sci. Univ. Kyoto, 31, pp. 219-239Panthee, M., A note on the unique continuation property for Zakharov-Kuznetsov equation (2004) Nonlinear Anal.Theory, Methods and Appl., 59 (3), pp. 425-438Panthee, M., Unique continuation property for the Kadomtsev-Petviashvili (KP-II) equation (2005) Electron. J. Diff. Equations, 2005 (59), pp. 1-12Saut, J.C., Scheurer, B., Unique continuation for some evolution equations (1987) J. Diff. Equations, 66, pp. 118-139Staffilani, G., On the generalized Korteweg-de Vries-type equations (1997) Diff. Int. Equations, 10 (4), pp. 777-796Tataru, D., Carleman type estimates and unique continuation for the Schrödinger equation (1995) Diff. Int. Equations, 8 (4), pp. 901-905Zhang, B., Unique continuation for the Korteweg-de Vries equation (1992) SIAM J. Math. Anal., 23, pp. 55-7
koamabayili/VECTRON-author-checklist: VECTRON author checklist
No full textWe have done our best to complete the author checklist relating to the use of animals in the hut study. Note that the objective for the hut study was to evaluate the IRS treatment applications for residual efficacy against Anopheles mosquitoes, including the local An. coluzzii mosquito population. Cows were only used to attract mosquitoes into the huts and no tests were carried out directly on the cows. The author checklist is intended for use with studies where experiments are carried out on animals, which is why we have had such difficulty in completing this for the hut study, as many of the questions do not relate to how the cows were used
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