A quasilinear parabolic system with nonlocal boundary condition.
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Chen, Botao, Mi, Yongsheng, Mu, Chunlai (2011)
Boundary Value Problems [electronic only]
Zhuan Ye (2015)
Annales Polonici Mathematici
This paper is dedicated to a regularity criterion for the 2D MHD equations and viscoelastic equations. We prove that if the magnetic field B, respectively the local deformation gradient F, satisfies for 1/p + 1/q = 1 and 2 < p ≤ ∞, then the corresponding local solution can be extended beyond time T.
Zhang, Hongwei, Hu, Qingying (2010)
Boundary Value Problems [electronic only]
Sahbi Keraani, Ana Vargas (2009)
Annales de l'I.H.P. Analyse non linéaire
Yvan Martel, Frank Merle, Pierre Raphaël (2011/2012)
Séminaire Laurent Schwartz — EDP et applications
These notes present the main results of [22, 23, 24] concerning the mass critical (gKdV) equation for initial data in close to the soliton. These works revisit the blow up phenomenon close to the family of solitons in several directions: definition of the stable blow up and classification of all possible behaviors in a suitable functional setting, description of the minimal mass blow up in , construction of various exotic blow up rates in , including grow up in infinite time.
Frank Merle, Pierre Raphael (2002)
Journées équations aux dérivées partielles
We consider the critical nonlinear Schrödinger equation with initial condition in dimension . For , local existence in time of solutions on an interval is known, and there exists finite time blow up solutions, that is such that . This is the smallest power in the nonlinearity for which blow up occurs, and is critical in this sense. The question we address is to understand the blow up dynamic. Even though there exists an explicit example of blow up solution and a class of initial data...
Yvan Martel, Frank Merle, Pierre Raphaël (2015)
Journal of the European Mathematical Society
We consider the mass critical (gKdV) equation for initial data in . We first prove the existence and uniqueness in the energy space of a minimal mass blow up solution and give a sharp description of the corresponding blow up soliton-like bubble. We then show that this solution is the universal attractor of all solutions near the ground state which have a defocusing behavior. This allows us to sharpen the description of near soliton dynamics obtained in [29].
Ali Hakem, Mohamed Berbiche (2013)
Publications de l'Institut Mathématique
Liu, Dengming, Mu, Chunlai (2010)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
Wang, Yulan, Xiang, Zhaoyin (2009)
Boundary Value Problems [electronic only]
Jing Li, Jingxue Yin, Chunhua Jin (2011)
Open Mathematics
This paper is mainly concerned with the blow-up and global existence profile for the Cauchy problem of a class of fully nonlinear degenerate parabolic equations with reaction sources.
Mohamed Ben Ayed, Khalil El Mehdi, Filomena Pacella (2006)
Annales de l'I.H.P. Analyse non linéaire
Amzoiu, Manuel (2010)
Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică
Shanshan Yang, Hongbiao Jiang, Yinhe Lin (2021)
Czechoslovak Mathematical Journal
We study compressible isentropic Navier-Stokes-Poisson equations in . With some appropriate assumptions on the density, velocity and potential, we show that the classical solution of the Cauchy problem for compressible unipolar isentropic Navier-Stokes-Poisson equations with attractive forcing will blow up in finite time. The proof is based on a contradiction argument, which relies on proving the conservation of total mass and total momentum.
Youpeng Chen, Baozhu Zheng (2015)
Annales Polonici Mathematici
This paper deals with the blow-up properties of positive solutions to a localized singular parabolic equation with weighted nonlocal nonlinear boundary conditions. Under certain conditions, criteria of global existence and finite time blow-up are established. Furthermore, when q=1, the global blow-up behavior and the uniform blow-up profile of the blow-up solution are described; we find that the blow-up set is the whole domain [0,a], including the boundary, in contrast to the case of parabolic equations...
Zhou, Jun (2009)
Applied Mathematics E-Notes [electronic only]
Jianwei Dong, Junhui Zhu, Yanping Wang (2020)
Czechoslovak Mathematical Journal
We will show the blow-up of smooth solutions to the Cauchy problems for compressible unipolar isentropic Navier-Stokes-Poisson equations with attractive forcing and compressible bipolar isentropic Navier-Stokes-Poisson equations in arbitrary dimensions under some restrictions on the initial data. The key of the proof is finding the relations between the physical quantities and establishing some differential inequalities.
Jing Lu (2013)
Applicationes Mathematicae
We give a sufficient condition under which the solutions of the energy-critical nonlinear wave equation and Schrödinger equation with inverse-square potential blow up. The method is a modified variational approach, in the spirit of the work by Ibrahim et al. [Anal. PDE 4 (2011), 405-460].
Xing Cheng, Yanfang Gao (2014)
Colloquium Mathematicae
The focusing nonlinear Schrödinger equation (NLS) with confining harmonic potential , is considered. By modifying a variational technique, we shall give a sufficient condition under which the corresponding solution blows up.
Yang Liu, Pengju Lv, Chaojiu Da (2016)
Annales Polonici Mathematici
This paper is concerned with the initial boundary value problem for a nonlocal p-Laplacian evolution equation with critical initial energy. In the framework of the energy method, we construct an unstable set and establish its invariance. Finally, the finite time blow-up of solutions is derived by a combination of the unstable set and the concavity method.
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