Unique global solution to the thermally radiative magnetohydrodynamics equations

2018 ◽  
Vol 69 (4) ◽  
Author(s):  
Peng Jiang
Keyword(s):  
Global Solution ◽  
Unique Global Solution ◽  
Magnetohydrodynamics Equations

Knudsen type group for time in ℝ and related Boltzmann type equations

2021 ◽  
pp. 2150072
Author(s):  
Jörg-Uwe Löbus
Keyword(s):  
Boundary Conditions ◽  
Global Solution ◽  
Physical Space ◽  
Type Equation ◽  
Collision Kernel ◽  
Unique Global Solution ◽  
Initial Value ◽  
Type Group ◽  
Diffusive Boundary ◽  
Diffusive Part

We consider certain Boltzmann type equations on a bounded physical and a bounded velocity space under the presence of both reflective as well as diffusive boundary conditions. We introduce conditions on the shape of the physical space and on the relation between the reflective and the diffusive part in the boundary conditions such that the associated Knudsen type semigroup can be extended to time [Formula: see text]. Furthermore, we provide conditions under which there exists a unique global solution to a Boltzmann type equation for time [Formula: see text] or for time [Formula: see text] for some [Formula: see text] which is independent of the initial value at time 0. Depending on the collision kernel, [Formula: see text] can be arbitrarily small.

scholarly journals GLOBAL SOLUTION FOR THE GENERALIZED ANISOTROPIC NAVIER–STOKES EQUATIONS WITH LARGE DATA

2015 ◽  
Vol 20 (2) ◽  
pp. 205-231 ◽  
Author(s):  
Daoyuan Fang ◽  
Bin Han
Keyword(s):  
Initial Data ◽  
Besov Space ◽  
Global Solution ◽  
Stokes Equations ◽  
Large Data ◽  
Navier Stokes ◽  
Unique Global Solution ◽  
Large Initial Data ◽  
Navier Stokes Equations ◽  
Anisotropic Besov Space

We are concerned with 3D incompressible generalized anisotropic Navier– Stokes equations with hyperdissipative term in horizontal variables. We prove that there exists a unique global solution for it with large initial data in anisotropic Besov space.

Genetic Algorithms in Multimodal Search Space

2011 ◽  
pp. 1621-1629
Author(s):  
Marcos Gestal ◽  
Julián Dorado
Keyword(s):  
Genetic Algorithms ◽  
Global Solution ◽  
Iterative Process ◽  
Search Space ◽  
Potential Solution ◽  
Unique Global Solution ◽  
Local Optima ◽  
Simple Interpretation ◽  
Precise Information ◽  
Local Solutions

Genetic algorithms (GAs) (Holland, 1975; Goldberg, 1989) try to find the solution for a problem using an initial group of individuals?the population?where each one represents a potential solution. Actually they are successfully applied in very different and actual fields (Yang, Shan, & Bui, 2008; Yu, Davis, Baydar, & Roy, 2008); nevertheless, GAs have some restrictions on a search space with more than a global solution or a unique global solution, together with multiple local optima. A classical GA faced with such a situation tends to focus the search on the surroundings of the global solution; however, it would be interesting to know a higher number of possible solutions for several reasons: precise information about the search space, easy implementation of the local solutions compared with the global one, simple interpretation of certain solutions compared with others, and so forth. To achieve that knowledge, an iterative process will be executed until reaching the desired goals. Such process will start with the grouping of the individuals into species that will independently search a solution in their environments; following, the crossover operation will involve individuals from different species in order not to leave unexplored any search space area. The process will be repeated according to the goals achieved.

Qualitative analysis of a parabolic–elliptic attraction–repulsion chemotaxis model with logistic source

2016 ◽  
Vol 09 (04) ◽  
pp. 1650051
Author(s):  
Haiyan Li ◽  
Jianguo Gao
Keyword(s):  
Fixed Point ◽  
Qualitative Analysis ◽  
Global Solution ◽  
Cell Mass ◽  
Logistic Source ◽  
Unique Global Solution ◽  
Chemotaxis Model ◽  
Initial Cell ◽  
Point Argument ◽  
Moser's Iteration

In this paper, we focus on the qualitative analysis of a parabolic–elliptic attraction–repulsion chemotaxis model with logistic source. Applying a fixed point argument, [Formula: see text]-estimate technique and Moser’s iteration, we derive that the model admits a unique global solution provided the initial cell mass satisfying [Formula: see text] for [Formula: see text] While for [Formula: see text], there are no restrictions on the initial cell mass and the result still holds.

scholarly journals Global solution to the incompressible Oldroyd-B model in hybrid Besov spaces

Filomat ◽  
2016 ◽  
Vol 30 (13) ◽  
pp. 3627-3639 ◽  
Author(s):  
Ruizhao Zia
Keyword(s):  
Cauchy Problem ◽  
Initial Data ◽  
Global Solution ◽  
Besov Spaces ◽  
Coupling Constant ◽  
Unique Global Solution ◽  
Small Initial Data ◽  
Nonlinear Anal ◽  
The Cauchy Problem

This paper is dedicated to the Cauchy problem of the incompressible Oldroyd-B model with general coupling constant ? ?(0,1). It is shown that this set of equations admits a unique global solution in a certain hybrid Besov spaces for small initial data in ?Hs ??Bd/2 2,1 with - d/2 < s < d2-1. In particular, if d ? 3, and taking s=0, then ?H0 ? ?Bd/2 2,1 = B d/2 2,1. Since Bt2,? ? Bd/2 2,1 if t > d/2, this result extends the work by Chen and Miao [Nonlinear Anal.,68(2008), 1928-1939].

scholarly journals Estimates of Solutions to Nonlinear Evolution Equations

2018 ◽  
Vol 14 (2) ◽  
pp. 7812-7817
Author(s):  
Alexander G. Ramm
Keyword(s):  
Banach Space ◽  
Global Solution ◽  
Nonlinear Operator ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Unique Global Solution ◽  
Estimates Of Solutions ◽  
Suitable Function

Consider the equation                  u’(t) = A (t, u (t)),   u(0)= U0 ;   u' := du/dt     (1).   Under some assumptions on the nonlinear operator A(t,u) it is proved that problem (1) has a unique global solution and this solution satisfies the following estimate                                               ||u (t)|| < µ (t) -1     for every t belongs to R+ = [0,infinity). Here µ(t) > 0,   µ belongs to  C1 (R+), is a suitable function and the norm ||u || is the norm in a Banach space X with the property ||u (t) ||’   <=  ||u’ (t) ||.

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