Fast Diffusion
Sharp decay estimates for the logarithmic fast diffusion equation and the Ricci flow on surfaces
... The theorem gives an interior sup bound for the logarithmic fast diffusion equation, depending only on the initial data, and not on the boundary behaviour of u at later times. This is in stark contrast to ...
17
Reverse Smoothing Effects, Fine Asymptotics, and Harnack Inequalities for Fast Diffusion Equations
... Theorem 3.1 adds to this asymptotic statement a more precise quantitative information that is valid not only for large times, but also for arbitrary small times. The solution thus inherits positivity and boundedness ...
31
Global Existence and Extinction of Weak Solutions to a Class of Semiconductor Equations with Fast Diffusion Terms
... We consider the transient drift-di ff usion model with fast di ff usion terms. This problem is not only degenerate but also singular. We first present existence result for general nonlinear diffusivities for the ...
14
Critical extinction exponents for a fast diffusion equation with nonlocal source and absorption
... a fast diffusion equation perturbed by both a nonlocal source term and an absorption term, which describes the diffusion of concentration of some Newtonian fluids or the density of some biological species (see [, ] ...
10
Extinction properties of solutions for a fast diffusion equation with nonlocal source
... In this paper, we investigate extinction properties of nonnegative nontrivial solutions for an initial boundary value problem of a fast diffusion equation with a nonlocal source in bounded domain. By using the ...
15
Critical Fujita exponents to a class of non-Newtonian filtration equations with fast diffusion
... )/n by blow-up subsolutions and global supersolutions. Recently, the same problem for an interesting variant of () is studied by the authors []. The non-Newtonian filtration equations with fast diffusion were ...
16
Critical curves for fast diffusion equations coupled via nonlinear boundary flux
... This paper is concerned with fast diffusion equations for coupling via nonlinear boundary flux. By means of the theory of linear equations and constructing self-similar super-solutions and sub-solutions, we obtain a ...
11
The critical exponent for fast diffusion equation with nonlocal source
... This paper is organized as follows. Section 2 concerns the non-global solution to prove Theorem 1.1. Section 3 deals with the global existence to prove Theorem 1.2. And Sect. 4 shows in what ways the parameter q of the ...
8
Combination of IVIM-DWI and 3D-ASL for differentiating true progression from pseudoprogression of Glioblastoma multiforme after concurrent chemoradiotherapy: study protocol of a prospective diagnostic trial
... motion diffusion-weighted imaging (IVIM-DWI) and three-dimensional arterial spin labeling imaging (3D-ASL) in differentiating true progression from pseudoprogression of ...apparent diffusion coefficient ...
7
A dynamic light scattering investigation into the dynamics of non ideal ternary polymer solutions : a thesis presented in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Physics at Massey University
... the fast diffusion coeffi cients which are within 5% of each other, the two slower diffusion coefficients are out by around ...three diffusion coefficients given by these two methods are ...
112
To the Properties of the Solutions of a Cross diffusion Parabolic System not in Divergence Form
... cross diffusion parabolic system not in divergence form with a source and a variable density based on comparison method is ...slow diffusion and fast diffusion cases are ...
7
Multimodality imaging and mathematical modelling of drug delivery to glioblastomas
... tissue diffusion coefficient – interact nonlinearly to produce the observed average tracer concentration in the ...and diffusion in the interstitial ...
21
Systems Modeling of Calcium Homeostasis and Mobilization in Platelets Mediated by Ip3 and Store-Operated Calcium Entry
... Our model for SOCE regulation consists of diffusion-limited dimerization of the calcium sensor STIM1, followed by fast, cytosolic calcium-dependent association of STIM1 dimers with Orai1[r] ...
100
Small diffusion and fast dying out asymptotics for superprocesses as non Hamiltonian quasiclassics for evolution equations
... u 0 = h −α φ 0 (x) exp {− S 0 (x)/h } , (1.16) where α > 0 is a constant and φ 0 , S 0 are smooth non-negative functions. From this asymptotics one can similarly obtain the corresponding asymptotics for the ...
17
Comparison Between Three-Dimensional Diffusion-Weighted PSIF Technique and Routine Imaging Sequences in Evaluation of Peripheral Nerves in Healthy People
... using diffusion gradients, the subcutaneous and fascial edema that limits the evalu- ation of small peripheral nerves (in particular distal to elbow and knee), selectively suppresses and accordingly increases the ...
7
Fast two-phase image segmentation based on diffusion equations and gray level sets
... oped fast algorithms [–] to the Chan-Vese image segmentation model to avoid these drawbacks ...developed fast algorithms based on calculating the variational energy of the Chan-Vese model directly ...
16
3T MR Imaging of Postoperative Recurrent Middle Ear Cholesteatomas: Value of Periodically Rotated Overlapping Parallel Lines with Enhanced Reconstruction Diffusion Weighted MR Imaging
... The ability of DWI to be used consistently to evaluate the temporal bone is hindered by image distortion caused by sus- ceptibility artifacts, chemical-shift artifacts, and ghosts in the phase-encoding direction. This is ...
5
A fast implicit difference scheme for a new class of time distributed order and space fractional diffusion equations with variable coefficients
... To overtake this shortcoming and get a faster convergence, some Krylov subspace meth- ods with circulant preconditioners have been studied and extended. Lei and Sun [45] de- veloped the preconditioned CGNR (PCGNR) method ...
24
Efficient segmentation based on Eikonal and diffusion equations
... The diffusion method performs well when images edges are strong and is robust to higher levels of image noise especially the noise that occurs at a single pixel as is commonly referred to as “salt and pepper” ...
14
Electrochemistry at highly oriented pyrolytic graphite (HOPG) : lower limit for the kinetics of outer sphere redox processes and general implications for electron transfer models
... cell assembled on freshly cleaved HOPG (within 3 s of cleavage), of different grades, with step edge density spanning up to 2 orders of magnitude. The processes are fast and close to reversible on all surfaces, ...
12