The Experts below are selected from a list of 31479 Experts worldwide ranked by ideXlab platform
E.g. Ladopoulos - One of the best experts on this subject based on the ideXlab platform.
-
petroleum reservoir engineering by non linear Singular Integral equations
Mechanical Engineering Research, 2011Co-Authors: E.g. LadopoulosAbstract:For the determination of the properties of several reservoir materials, when oil reserves are moving through porous media, a new mathematical approach is proposed. Such problem is very much important for petroleum reservoir engineering. Thus, the above mentioned problem is reduced to the solution of a non-linear Singular Integral equation, which is numerically evaluated by using the Singular Integral Operators Method (S.I.O.M.). Beyond the above, several properties are analyzed and investigated for the porous medium equation, defined as a Helmholtz differential equation. Finally, an application is given for a well testing to be checked when an heterogeneous oil reservoir is moving in a porous medium. Hence, by using the S.I.O.M., then the pressure response from the well test conducted in the above heterogeneous oil reservoir, is numerically calculated and investigated.
-
non linear Singular Integral representation for petroleum reservoir engineering
Acta Mechanica, 2011Co-Authors: E.g. LadopoulosAbstract:A new mathematical model is proposed in order to determine the properties of the reservoir materials, when oil reserves are moving through porous media, which is a very important problem of petroleum reservoir engineering. Thus, the above problem is reduced to the solution of a non-linear Singular Integral equation, which is numerically evaluated by using the Singular Integral operators method (SIOM). Also, several properties of the porous medium equation, which is a Helmholtz differential equation, are analyzed and investigated. An application is finally given for a well testing to be checked when an heterogeneous oil reservoir is moving in a porous medium. By using the SIOM, the pressure response from the well test conducted in the above heterogeneous oil reservoir is calculated.
-
Singular Integral equations linear and non linear theory and its applications in science and engineering
2000Co-Authors: E.g. LadopoulosAbstract:1 - Introduction.- 2 - Finite-Part Singular Integral Equations.- 3 - Finite-Part Singular Integral Equations in Elasticity and Fracture Mechanics.- 4 - Singular Integral Equations in Aerodynamics.- 5 - Multidimensional Singular Integral Equations.- 6 - Multidimensional Singular Integral Equations in Elasticity and Fracture Mechanics of Isotropic Solids.- 7 - Multidimensional Singular Integral Equations in Relativistic Elastic Stress Analysis for Moving Frames.- 8 - Multidimensional Singular Integral Equations in Elasticity and Fracture Mechanics of Anisotropic Solids.- 9 - Multidimensional Singular Integral Equations in Plasticity of Isotropic Solids.- 10 - Non-Linear Singular Integral Equations.- 11 - Numerical Evaluation Methods for Non-Linear Singular Integral Equations.- 12 - Non-Linear Singular Integral Equations in Fluid Mechanics.- 13 - Non-Linear Integro-Differential Equations in Structural Analysis.- 14 - Non-Linear Singular Integral Equations in Elastodynamics.- 15 - Conclusions.- Appendix - Mathematical Definitions.- Author Index.
-
Finite-Part Singular Integral Equations
Singular Integral Equations, 2000Co-Authors: E.g. LadopoulosAbstract:Finite-part Singular Integral equations are recently widely applicable in many important problems of engineering mechanics, like elasticity, plasticity, fracture mechanics and aerodynamics. The general property of this type of Singular Integral equations, consists to the generalization of the Cauchy Singular Integral equations, which have been systematically studied during the last decades.
-
Singular Integral Equations in Aerodynamics
Singular Integral Equations, 2000Co-Authors: E.g. LadopoulosAbstract:Finite-part Singular Integral equations are further widely applicable in other important problems of engineering mechanics, like aerodynamics. Hence, it is of interest to solve numerically the systems of the Singular Integral equations of the respective boundary value problem, instead of the problem itself.
Juan Verdera Melenchón - One of the best experts on this subject based on the ideXlab platform.
-
Estimates for the maximal Singular Integral in terms of the Singular Integral: the case of even kernels
Annals of Mathematics, 2011Co-Authors: Joan Mateu Bennassar, Joan Orobitg I Huguet, Juan Verdera MelenchónAbstract:Let T be a smooth homogeneous Calder on-Zygmund Singular Integral operator in R n . In this paper we study the problem of controlling the maximal Singular Integral T ? f by the Singular Integral Tf. The most basic form of control one may consider is the estimate of the L 2 (R n ) norm of T ? f by a constant times the L 2 (R n ) norm of Tf. We show that if T is an even higher order Riesz transform, then one has the stronger pointwise inequality T ? f(x) C M(Tf)(x), where C is a constant and M is the Hardy-Littlewood maximal operator. We prove that the L 2 estimate of T ? by T is equivalent, for even smooth homogeneous Calder on-Zygmund operators, to the pointwise inequality between T ? and M(T ). Our main result characterizes the L 2 and pointwise inequalities in terms of an algebraic condition expressed in terms of the kernel ( x) jxjn of T , where is an
Qingying Xue - One of the best experts on this subject based on the ideXlab platform.
-
On the Composition of Rough Singular Integral Operators
The Journal of Geometric Analysis, 2020Co-Authors: Xudong Lai, Qingying XueAbstract:In this paper, we investigate the behavior of the bounds of the composition for rough Singular Integral operators on the weighted space. More precisely, we obtain the quantitative weighted bounds of the composite operator for two Singular Integral operators with rough homogeneous kernels on $$L^p({\mathbb {R}}^d,\,w)$$, $$p\in (1,\,\infty )$$, which is smaller than the product of the quantitative weighted bounds for these two rough Singular Integral operators. Moreover, at the endpoint $$p=1$$, the $$L\log L$$ weighted weak-type bound is also obtained, which has interests of its own in the theory of rough Singular Integral even in the unweighted case.
-
On the composition for rough Singular Integral operators
arXiv: Classical Analysis and ODEs, 2018Co-Authors: Xudong Lai, Qingying XueAbstract:In this paper, we investigate the behavior of the bounds of the composition for rough Singular Integral operators on the weighted space. More precisely, we obtain the quantitative weighted bounds of the composite operator for two Singular Integral operators with rough homogeneous kernels on $L^p(\mathbb{R}^d,\,w)$, $p\in (1,\,\infty)$, which is smaller than the product of the quantitative weighted bounds for these two rough Singular Integral operators. Moreover, at the endpoint $p=1$, the $L\log L$ weighted weak type bound is also obtained, which has interests of its own in the theory of rough Singular Integral even in the unweighted case.
Swanhild Bernstein - One of the best experts on this subject based on the ideXlab platform.
-
Monotonicity principles for Singular Integral equations in Clifford analysis
arXiv: Complex Variables, 1998Co-Authors: Swanhild BernsteinAbstract:Monotonicity principles can be used to get informations about nonlinear Singular Integral equations. These results are based on a theorem of Browder and Minty. We consider a family of monotone Singular Integral operators and associated nonlinear Singular Integral equations with Nemickii operator in Clifford analysis which has an application to the nonlinear magnetic field equation in the 3-dimensional Euclidean space.
-
Symbol and characteristic of weakly Singular Integral operators
Applicable Analysis, 1993Co-Authors: Swanhild BernsteinAbstract:A basic notion of pseudodifferential operators or Singular Integral operators is the symbol. We want to give a formula for the symbol of weakly Singular Integral operators. This gives a simple connection between weakly Singular Integral operators and a special class of pseudodifferential operators. The case of Singular Integral operators is included. In this way we are able to use the theory of symbols also for weakly Singular Integral operators.
Joan Mateu Bennassar - One of the best experts on this subject based on the ideXlab platform.
-
Estimates for the maximal Singular Integral in terms of the Singular Integral: the case of even kernels
Annals of Mathematics, 2011Co-Authors: Joan Mateu Bennassar, Joan Orobitg I Huguet, Juan Verdera MelenchónAbstract:Let T be a smooth homogeneous Calder on-Zygmund Singular Integral operator in R n . In this paper we study the problem of controlling the maximal Singular Integral T ? f by the Singular Integral Tf. The most basic form of control one may consider is the estimate of the L 2 (R n ) norm of T ? f by a constant times the L 2 (R n ) norm of Tf. We show that if T is an even higher order Riesz transform, then one has the stronger pointwise inequality T ? f(x) C M(Tf)(x), where C is a constant and M is the Hardy-Littlewood maximal operator. We prove that the L 2 estimate of T ? by T is equivalent, for even smooth homogeneous Calder on-Zygmund operators, to the pointwise inequality between T ? and M(T ). Our main result characterizes the L 2 and pointwise inequalities in terms of an algebraic condition expressed in terms of the kernel ( x) jxjn of T , where is an
