The propagation of singularities for the system of homogeneous thermoelasticity in one space dimension is studied. Linear and a class of semilinear Cauchy problems are considered.

Recall that a metric space M is said to be complete if every Cauchy sequence in M converges to a limit in M . Not all metric spaces are complete, but it is a fact that all metric spaces can be “completed”, in a way that preserves the essential structure of the metric space. If the space in question is a normed linear space this process completes the space to a Banach space, and an inner product...

and Applied Analysis 3 Mu et al. 19 studied the secondary critical exponent for the following p-Laplacian equation with slow decay initial values: ut div ( |∇u|p−2∇u ) u, x, t ∈ R × 0, T , u x, 0 u0 x , x ∈ R, 1.6 where p > 2, q > 1, and showed that, for q > q∗ c p − 1 p/N , there exists a secondary critical exponent ac p/ q 1 − p such that the solution u x, t of 1.6 blows up in finite time for...

K e y w o r d s P a r a b o l i c equations, Cauchy-Dirichlet problem. 1. I N T R O D U C T I O N Let Z; be a l inear parabol ic opera to r of the form, x lx j i,j=l i=1 ! ! ] ~n -F1 . w h e r e x = (xt , t) ---( x l , x 2 , . . . ,X/n,t) C Let f~ C ]R ~ be a bounded C 1,1 domain and QT, the cylinder ft × (0, T) . Aim of this note is to s tudy the Cauchy-Dir ichle t problem, Z:u = f , a.e. x C ...

We explore two generalizations of the Cauchy-Schwarz Bessel’s inequality and the Selberg inequality and their application to probability theory. We then give a tautological proof of the De Caen-Selberg Inequality and a proof of the second Borel-Cantelli Lemma with negative dependence. We finish with a suggestion of how linear operator theory can help us understand the tightness of many Selberg-...

The purpose of this paper is to prove that every sequence of closed approximable measures defined on the Borelfield of a normal topological space with values in an abelian topological group is Cauchy convergent for all Borel sets if it is Cauchy convergent for all regular open sets. In particular every sequence of measures on the Borel-field of a perfectly normal topological space which is Cauc...

In the present paper, we study time-space fractional diffusion equation involving Caputo differential operator and Laplacian. This describes Lévy flight with Brownian motion component drift component. First, asymptotic behavior of fundamental solution is considered. Then, use to obtain representation formula solutions Cauchy problem. last, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML...

We show that any solution of the two-dimensional Navier-Stokes equation whose vorticity distribution is uniformly bounded in L(R) for positive times is entirely determined by the trace of the vorticity at t = 0, which is a finite measure. When combined with previous existence results by Cottet, by Giga, Miyakawa, and Osada, and by Kato, this uniqueness property implies that the Cauchy problem f...

Description The package implements the statistical theory of L-moments including L-moment estimation, probability-weighted moment estimation, parameter estimation for numerous familiar and not-so-familiar distributions, and L-moment estimation for the same distributions from the parameters. L-moments are derived from the expectations of order statistics and are linear with respect to the probab...

This article contains a natural and important application of the holomorphic support functions for convex domains of finite type in Cn constructed in [DiFo]. Namely, we use these functions to get ∂-solving Cauchy-Fantappié kernels for ∂-closed (0, q)-forms, such that the solutions given by them on bounded forms satisfy the best possible uniform Hölder estimates. More precisely we show: Theorem ...