共查询到20条相似文献,搜索用时 15 毫秒
1.
Ricardo Abreu Blaya Juan Bory Reyes Dixan Peña Peña Frank Sommen 《Advances in Applied Clifford Algebras》2007,17(2):145-152
Starting with an integral representation for the class of continuously differentiable solutions
of the system
where
is the complex Clifford algebra constructed over
are some suitable Clifford vectors and
their corresponding Dirac operators, we define the isotonic Cauchy transform and establish the Sokhotski-Plemelj formulae.
Some consequences of this result are also derived. 相似文献
2.
Let ∑ be either an oriented hyperplane or the unit sphere in
, let
be open and connected and let
be an open and connected domain in
such that
. If in
is a null solution of the Dirac operator (also called a monogenic function in
) which is continuously extendable to
, then conditions upon
are given enabling the monogenic extension of
across
. In such a way Schwarz reflection type principles for monogenic functions are established in the Spin (1) and Spin
cases. The Spin (1) case includes the classical Schwarz reflection principle for holomorphic functions in the plane. The
Spin
case deals with so-called “half boundary value problems” for the Dirac operator.
Received: 2 February 2006 相似文献
3.
Victor Palamodov 《Advances in Applied Clifford Algebras》2009,19(2):417-425
The paper addresses the Levi problem for a system of n Fueter equations in a domain in quaternionic space . This problem relates to various conditions of convexity and pseudoconvexity of the boundary of the domain.
Received: October, 2007, Accepted: February, 2008. 相似文献
4.
We establish a priori estimates for solutions to ultraparabolic equations which play a crucial role in the solvability of
the initial value problem. A class of these equations came from population dynamics, namely from a fish larvae model.
相似文献
5.
Sadek Gala 《Archiv der Mathematik》2007,88(5):448-454
In this note, we will give another proof of the uniqueness of mild solutions to the Navier-Stokes equations in the class C([0,∞);
by a simple application of Giga-Shor’s L
p
− L
q
(time-space) estimates, i.e., integral norms in the time variable. The proof relies on a method introduced by S. Monniaux
[9] to prove the same result.
Received: 11 June 2006 相似文献
6.
G. P. Galdi K. Pileckas A. L. Silvestre 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2007,58(6):994-1007
We show that in an unsteady Poiseuille flow of a Navier–Stokes fluid in an infinite straight pipe of constant cross-section,
σ, the flow rate, F(t), and the axial pressure drop, q(t), are related, at each time t, by a linear Volterra integral equation of the second type, where the kernel depends only upon t and σ. One significant consequence of this result is that it allows us to prove that the inverse parabolic problem of finding a
Poiseuille flow corresponding to a given F(t) is equivalent to the resolution of the classical initial-boundary value problem for the heat equation.
G. P. Galdi: Partially supported by the NSF grant DMS–0404834.
K. Pileckas: Supported by EC FP6 MCToK program SPADE2, MTKD–CT–2004–014508
A. L. Silvestre: Supported by FCT-Project POCI/MAT/61792/2004 相似文献
7.
We prove that the Cauchy problem for a hyperbolic, homogeneous equation with
coefficients depending on time, is well posed in every Gevrey class, although in general it is not well-posed in
provided the characteristic roots satisfy the condition
相似文献
8.
Elena I. Kaikina Leonardo Guardado-Zavala Hector F. Ruiz-Paredes Jesus A. Mendez Navarro 《NoDEA : Nonlinear Differential Equations and Applications》2009,16(1):63-77
We study nonlinear nonlocal equations on a half-line in the critical case
where . The linear operator is a pseudodifferential operator defined by the inverse Laplace transform with dissipative symbol , the number . The aim of this paper is to prove the global existence of solutions to the inital-boundary value problem (0.1) and to find
the main term of the large time asymptotic representation of solutions in the critical case.
相似文献
9.
Universal Laurent series where the universal approximation is valid on the boundary of the multiple connected open Ω appears
for the first time in [2]. We show that it is possible to demand universal approximation only to a part of the boundary while
on the remaining part the universal function can be smooth.
Received: 29 May 2007 相似文献
10.
Luo Wu Huizhao Liu Zongyao Wang 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2008,59(4):619-633
This paper interests a system for the non-Newtonian flow in the whole space. [14] estimated decay of it as t tends to infinity. The aim of the paper is to investigate decay problem of it and to improve a result of [14].
相似文献
11.
Given a connected open set
and a function w ∈LN/p(Ω) if 1 < p < N and w ∈Lr (Ω) for some r ∈(1, ∞) if p ≧ N, with
we prove that the positive principal eigenvalue of the problem
is unique and simple. This improves previous works all of which assumed w in a smaller space than LN/p (Ω) to ensure that Harnack’s inequality holds. Our proof does not rely on Harnack’s inequality, which may fail in our case.
Received: 18 March 2005; revised: 7 April 2005 相似文献
12.
Let be open, let be the Dirac operator in and let be the Clifford algebra constructed over the quadratic space . If for fixed, denotes the space of r-vectors in , then an -valued smooth function W = W
r
+ W
r+2 in Ω is said to satisfy the Moisil-Théodoresco system if . In terms of differential forms, this means that the corresponding - valued smooth form w = w
r
+ w
r+2 satisfies in Ω the system d
*
w
r
= 0, dw
r
+ d
*
w
r+2 = 0; dw
r+2 = 0.
Based on techniques and results concerning conjugate harmonic functions in the framework of Clifford analysis, a structure
theorem is proved for the solutions of the Moisil-Théodoresco system.
相似文献
13.
Constantin Buşe Mihail Megan Manuela-Suzy Prajea Petre Preda 《Integral Equations and Operator Theory》2007,59(4):491-500
Among others we shall prove that an exponentially bounded evolution family U = {U(t, s)}
t≥s≥0 of bounded linear operators acting on a Banach space X is uniformly exponentially stable if and only if there exists q
[1, ∞) such that
This result seems to be new even in the finite dimensional case and it is the strong variant of an old result of E. A. Barbashin
([1]Theorem 5.1).
The first author was partially supported by the CNCSIS’s grant no. 546/2006. 相似文献
14.
Adimurthi Jacques Giacomoni 《NoDEA : Nonlinear Differential Equations and Applications》2005,12(1):1-20
This paper deals with the existence and the behaviour of global connected branches of positive solutions of the problem
We consider a function h which is smooth and changes sign. 相似文献
15.
The aim of this paper is to give the basic principles of hyperbolic function theory on the Clifford algebra . The structure of the theory is quite similar to the case of Clifford algebras with negative generators, but the proofs are
not obvious. The (real) Clifford algebra is generated by unit vectors with positive squares e2i = + 1. The hyperbolic Dirac operator is of the form where Q0f is represented by the composition . If is a solution of Hkf = 0, then f is called k-hypergenic in Ω, where is an open set. We introduce some basic results of hyperbolic function theory and give some representation theorems on .
Received: October, 2007. Accepted: February, 2008. 相似文献
16.
Nele De Schepper 《Advances in Applied Clifford Algebras》2009,19(2):253-268
By applying a method introduced by De Bie and Sommen in Clifford superanalysis, the orthogonality relations of the generalized
Clifford–Gegenbauer polynomials of wavelet analysis are extended. Moreover, this new approach allows for proving new important
properties of these polynomials, such as an annihilation equation, a differential equation and an expression in terms of the
Jacobi polynomials on the real line.
This paper is dedicated to the memory of our friend and colleague Jarolim Bureš 相似文献
17.
18.
Our first basic model is the fully nonlinear dual porous medium equation with source
for which we consider the Cauchy problem with given nonnegative bounded initial data u0. For the semilinear case m=1, the critical exponent
was obtained by H. Fujita in 1966. For p ∈(1, p0] any nontrivial solution blows up in finite time, while for p > p0 there exist sufficiently small global solutions. During last thirty years such critical exponents were detected for many
semilinear and quasilinear parabolic, hyperbolic and elliptic PDEs and inequalities. Most of efforts were devoted to equations
with differential operators in divergent form, where classical techniques associated with weak solutions and integration by
parts with a variety of test functions can be applied. Using this fully nonlinear equation, we propose and develop new approaches
to calculating critical Fujita exponents in different functional settings.
The second models with a “semi-divergent” diffusion operator is the thin film equation with source
for which the critical exponent is shown to be
相似文献
19.
Alessandro Perotti 《Advances in Applied Clifford Algebras》2009,19(2):441-451
We study Fueter-biregular functions of one quaternionic variable. We consider left-regular functions in the kernel of the
Cauchy–Riemann operator
. A quaternionic function is biregular if on Ω, f is invertible and . Every continuous map p from Ω to the sphere of unit imaginary quaternions induces an almost complex structure Jp on the tangent bundle of . Let be the space of (pseudo)holomorphic maps from (Ω, Jp) to (), where Lp is the almost complex structure defined by left multiplication by p. Every element of is regular, but there exist regular functions that are not holomorphic for any p. The space of biregular functions contains the invertible elements of the spaces . By means of a criterion, based on the energy-minimizing property of holomorphic maps, that characterizes holomorphic functions
among regular functions, we show that every biregular function belongs to some space .
Received: October, 2007. Accepted: February, 2008. 相似文献
20.
In this paper we give a generalization of the classical Borel–Carathéodory theorem in complex analysis to higher dimensions
in the framework of Quaternionic Analysis.
Submitted: November 14, 2007., Revised: February 25, 2008. 相似文献