排序方式: 共有57条查询结果,搜索用时 0 毫秒
51.
This paper considers a fast diffusion equation with potential ut= um V (x)um+upin Rn×(0,T), where 1 2αm+n< m ≤ 1, p > 1, n ≥ 2, V (x) ~ω|x|2with ω≥ 0 as |x| →∞,and α is the positive root of αm(αm + n 2) ω = 0. The critical Fujita exponent was determined as pc= m +2αm+nin a previous paper of the authors. In the present paper,we establish the second critical exponent to identify the global and non-global solutions in their co-existence parameter region p > pcvia the critical decay rates of the initial data.With u0(x) ~ |x| aas |x| →∞, it is shown that the second critical exponent a =2p m,independent of the potential parameter ω, is quite different from the situation for the critical exponent pc. 相似文献
52.
By the typical Knoevenagel condensation of Bodipy with aldehyde derivatives, two novel Bodipy derivatives 3 and 6 with symmetric three and six alkyl chains were designed and prepared. The Bodipy derivative 3 with three alkyl chains showed no mesophase but the Bodipy derivative 6 with six alkyl chains possessed the orderly hexagonal columnar mesophase at room temperature. Both samples 3 and 6 exhibited the near-infrared fluorescence with high fluorescence quantum yields and larger Stokes shifts than their Bodipy precursors. Sample 6 was the first near-infrared fluorescent columnar liquid crystal with Bodipy core. This research presented a good strategy on constructing the near-infrared columnar Bodipy liquid crystal. 相似文献
53.
54.
Geometric singularities, such as cusps and self-intersecting surfaces, are major obstacles to the accuracy, convergence, and stability of the numerical solution of the Poisson-Boltzmann (PB) equation. In earlier work, an interface technique based PB solver was developed using the matched interface and boundary (MIB) method, which explicitly enforces the flux jump condition at the solvent-solute interfaces and leads to highly accurate biomolecular electrostatics in continuum electric environments. However, such a PB solver, denoted as MIBPB-I, cannot maintain the designed second order convergence whenever there are geometric singularities, such as cusps and self-intersecting surfaces. Moreover, the matrix of the MIBPB-I is not optimally symmetrical, resulting in the convergence difficulty. The present work presents a new interface method based PB solver, denoted as MIBPB-II, to address the aforementioned problems. The present MIBPB-II solver is systematical and robust in treating geometric singularities and delivers second order convergence for arbitrarily complex molecular surfaces of proteins. A new procedure is introduced to make the MIBPB-II matrix optimally symmetrical and diagonally dominant. The MIBPB-II solver is extensively validated by the molecular surfaces of few-atom systems and a set of 24 proteins. Converged electrostatic potentials and solvation free energies are obtained at a coarse grid spacing of 0.5 A and are considerably more accurate than those obtained by the PBEQ and the APBS at finer grid spacings. 相似文献
55.
Xueli BaiShuangshuang Zhou Sining Zheng 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(7):2508-2514
This paper studies the Cauchy problem for the fast diffusion equation with a localized reaction. We establish the Fujita type theorem to the problem, and then obtain the diffusion-independent blow-up rate for the non-global solutions. Moreover, we prove that the blow-up set for the problem consists of a single point under large initial data. These conclusions are quite different from those for the slow diffusion case. 相似文献
56.
Fengjie Li Bingchen Liu Sining Zheng 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2007,24(10):717-735
This paper deals with simultaneous and non-simultaneous blow-up for heat equations coupled via nonlinear boundary fluxes
\frac?u?h = um + vp, \frac?v?h = uq + vn\frac{\partial u}{\partial\eta} = u^{m} + v^{p}, \frac{\partial v}{\partial\eta} = u^{q} + v^{n} 相似文献
57.
|