On the order of pointwise convergence of some boundary element methods. Part I. Operators of negative and zero order
On the Origin of Chaos in the Belousov-Zhabotinsky Reaction in Closed and Unstirred Reactors
We investigate the origin of deterministic chaos in the Belousov–Zhabotinsky (BZ) reaction carried out in closed and unstirred reactors (CURs). In detail, we develop a model on the idea that hydrodynamic instabilities play a driving role in the transition to chaotic dynamics. A set of partial differential equations were derived by coupling the two variable Oregonator–diffusion system to the Navier–Stokes equations. This approach allows us to shed light on the correlation between chemical oscillations...
On the oscillation of forced second order mixed-nonlinear elliptic equations
Oscillation theorems are established for forced second order mixed-nonlinear elliptic differential equations ⎧ , ⎨ ⎩ under quite general conditions. These results are extensions of the recent results of Sun and Wong, [J. Math. Anal. Appl. 334 (2007)] and Zheng, Wang and Han [Appl. Math. Lett. 22 (2009)] for forced second order ordinary differential equations with...
On the oscillation of solutions of parabolic partial functional differential equations
On the oscillation of some impulsive parabolic equations with several delays
In this paper, several oscillation criteria are established for some nonlinear impulsive functional parabolic equations with several delays subject to boundary conditions. We shall mainly use the divergence theorem and some corresponding impulsive delayed differential inequalities.
On the -growth of entire function solutions of Helmholtz equation.
On the Paneitz energy on standard three sphere
We prove that the Paneitz energy on the standard three-sphere is bounded from below and extremal metrics must be conformally equivalent to the standard metric.
On the Paneitz energy on standard three sphere
We prove that the Paneitz energy on the standard three-sphere S3 is bounded from below and extremal metrics must be conformally equivalent to the standard metric.
On the parabolic potentials in degenerate-type heat equation.
On the parabolic-elliptic limit of the doubly parabolic Keller-Segel system modelling chemotaxis
We establish new results on convergence, in strong topologies, of solutions of the parabolic-parabolic Keller-Segel system in the plane to the corresponding solutions of the parabolic-elliptic model, as a physical parameter goes to zero. Our main tools are suitable space-time estimates, implying the global existence of slowly decaying (in general, nonintegrable) solutions for these models, under a natural smallness assumption.
On the parabolic-elliptic Patlak-Keller-Segel system in dimension 2 and higher
This review is dedicated to recent results on the 2d parabolic-elliptic Patlak-Keller-Segel model, and on its variant in higher dimensions where the diffusion is of critical porous medium type. Both of these models have a critical mass such that the solutions exist globally in time if the mass is less than and above which there are solutions which blowup in finite time. The main tools, in particular the free energy, and the idea of the methods are set out. A number of open questions are also...
On the parallel domain decomposition algorithms for time-dependent problems.
On the parameter dependence of solutions to the ...-equation.
On the parameter in augmented Lagrangian preconditioning for isogeometric discretizations of the Navier-Stokes equations
In this paper, we deal with the optimal choice of the parameter for augmented Lagrangian preconditioning of GMRES method for efficient solution of linear systems obtained from discretization of the incompressible Navier-Stokes equations. We consider discretization of the equations using the B-spline based isogeometric analysis approach. We are interested in the dependence of the convergence on the parameter for various problem parameters (Reynolds number, mesh refinement) and especially for...
On the Partial Regularity of Weak Solutions of Nonlinear Parabolic Systems.
On the p-biharmonic operator with critical Sobolev exponent
We study the existence of solutions for a p-biharmonic problem with a critical Sobolev exponent and Navier boundary conditions, using variational arguments. We establish the existence of a precise interval of parameters for which our problem admits a nontrivial solution.
On the PC-ansatz.
On the penalized obstacle problem in the unit half ball.
On the periodic KdV equation in weighted Sobolev spaces
On the persistence of decorrelation in the theory of wave turbulence
We study the statistical properties of the solutions of the Kadomstev-Petviashvili equations (KP-I and KP-II) on the torus when the initial datum is a random variable. We give ourselves a random variable with values in the Sobolev space with big enough such that its Fourier coefficients are independent from each other. We assume that the laws of these Fourier coefficients are invariant under multiplication by for all . We investigate about the persistence of the decorrelation between the...