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Journal of Mathematical Physics, ISSN 0022-2488, 07/2018, Volume 59, Issue 7
We study the dynamical properties of blowup solutions to the focusing L-2-supercritical nonlinear fractional Schrodinger equation i partial derivative(t)u -... 
PHYSICS, MATHEMATICAL | CAUCHY-PROBLEM
Journal Article
Nonlinear Analysis, Theory, Methods & Applications, ISSN 0362-546X, 01/2014, Volume 95, pp. 38 - 49
This article proves the ill-posedness of the Cauchy problem for the two-dimensional KelleraSegel model in TriebelaLizorkin spaces, FI2a1,r(R2) for... 
Cauchy problem
Journal Article
Nonlinear Analysis, Theory, Methods & Applications, ISSN 0362-546X, 01/2014, Volume 95, pp. 499 - 529
It is shown that the initial value problem for the FokasaOlveraRosenauaQiao equation (FORQ) is well-posed in Sobolev spaces HsHs, s>5/2s>5/2, in the sense of... 
Cauchy problem
Journal Article
Nonlinear Analysis, Theory, Methods & Applications, ISSN 0362-546X, 01/2014, Volume 95, pp. 691 - 702
This paper is concerned with the Cauchy problem of a nonlocal equation that takes into account convective and pp-Laplacian diffusive effects 
Cauchy problem
Journal Article
Nonlinear Analysis, Theory, Methods & Applications, ISSN 0362-546X, 01/2014, Volume 95, pp. 107 - 116
This paper deals with a new integrable two-component CamassaaHolm (CH2) system which describes the motion of fluid. We are concerned with discovering the wave... 
Cauchy problem
Journal Article
Nonlinear Analysis, Theory, Methods & Applications, ISSN 0362-546X, 09/2013, Volume 88, pp. 1 - 15
In this paper, we study the Cauchy problem for the two-component DullinaGottwaldaHolm system with the initial data (u0,I0)aBp,rs(R)ABp,rsa1(R),1aOp,raO+a, and... 
Cauchy problem
Journal Article
Nonlinear Analysis, Theory, Methods & Applications, ISSN 0362-546X, 07/2013, Volume 85, pp. 52 - 65
The Cauchy problem for the BGK equation with two kinds of force fields is studied in this paper. The first one considers a given force field F(t,x,v)F(t,x,v)... 
Cauchy problem
Journal Article
Nonlinear Analysis, Theory, Methods & Applications, ISSN 0362-546X, 07/2013, Volume 85, pp. 52 - 65
The Cauchy problem for the BGK equation with two kinds of force fields is studied in this paper. The first one considers a given force field F(t.x, v) which is... 
Cauchy problem
Journal Article
Journal fur die Reine und Angewandte Mathematik, ISSN 0075-4102, 03/2008, Volume 616, Issue 616, pp. 15 - 46
In this paper we derive new simple estimates for ordinary differential equations with Sobolev coefficients. These estimates not only allow to recover some old... 
MATHEMATICS | CAUCHY-PROBLEM
Journal Article
2007, OXFORD MATHEMATICAL MONOGRAPHS., ISBN 9780199211234, Volume 9780199211234, 535
Authored by leading scholars, this comprehensive, self-contained text presents a view of the state of the art in multi-dimensional hyperbolic partial... 
Differential equations, Partial | Mathematics | applied mathematics | Linear problem | Shock waves | Nonlinear problem | Cauchy problem
Book
Communications in Partial Differential Equations, ISSN 0360-5302, 01/2019, Volume 44, Issue 7, p. 613
In this article, we consider the Cauchy problem for isometric immersions. More precisely, given a smooth isometric immersion of a codimension one submanifold,... 
Submerging | Manifolds (mathematics) | Cauchy problem
Journal Article
ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE, ISSN 0391-173X, 2019, Volume 19, Issue 1, pp. 217 - 251
We prove Gevrey well posedness of the Cauchy problem for general linear systems whose principal symbol is hyperbolic and coefficients are sufficiently Gevrey... 
MATHEMATICS | CAUCHY-PROBLEM
Journal Article
2011, Posebna izdanja, ISBN 9788680593456, Volume 23, vi, 352
Book
manuscripta mathematica, ISSN 0025-2611, 07/2019, Volume 159, Issue 3-4, p. 379
In this paper, our main aim is to derive L.sup.p-L.sup.q L p - L q estimates of the solution u.sub.k(x,t) u k ( x , t ) (t fixed) of the Cauchy problem for the... 
Journal Article
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