The Experts below are selected from a list of 321 Experts worldwide ranked by ideXlab platform

R. Triggiani - One of the best experts on this subject based on the ideXlab platform.

  • l2 σ regularity of the Boundary to Boundary Operator b l for hyperbolic and petrowski pdes
    Abstract and Applied Analysis, 2003
    Co-Authors: I. Lasiecka, R. Triggiani
    Abstract:

    This paper takes up and thoroughly analyzes a technical mathematical issue in PDE theory, while—as a by-pass product—making a larger case. The technical issue is the L 2 ( Σ ) -regularity of the Boundary → Boundary Operator B ∗ L for (multidimensional) hyperbolic and Petrowski-type mixed PDEs problems, where L is the Boundary input → interior solution Operator and B is the control Operator from the Boundary. Both positive and negative classes of distinctive PDE illustrations are exhibited and proved. The larger case to be made is that hard analysis PDE energy methods are the tools of the trade—not soft analysis methods. This holds true not only to analyze B ∗ L , but also to establish three inter-related cardinal results: optimal PDE regularity, exact controllability, and uniform stabilization. Thus, the paper takes a critical view on a spate of “abstract” results in “infinite-dimensional systems theory,” generated by unnecessarily complicated and highly limited “soft” methods, with no apparent awareness of the high degree of restriction of the abstract assumptions made—far from necessary—as well as on how to verify them in the case of multidimensional dynamical systems such as PDEs.

  • L2(Σ)-regularity of the Boundary to Boundary Operator B∗L for hyperbolic and Petrowski PDEs
    Abstract and Applied Analysis, 2003
    Co-Authors: I. Lasiecka, R. Triggiani
    Abstract:

    This paper takes up and thoroughly analyzes a technical mathematical issue in PDE theory, while—as a by-pass product—making a larger case. The technical issue is the L 2 ( Σ ) -regularity of the Boundary → Boundary Operator B ∗ L for (multidimensional) hyperbolic and Petrowski-type mixed PDEs problems, where L is the Boundary input → interior solution Operator and B is the control Operator from the Boundary. Both positive and negative classes of distinctive PDE illustrations are exhibited and proved. The larger case to be made is that hard analysis PDE energy methods are the tools of the trade—not soft analysis methods. This holds true not only to analyze B ∗ L , but also to establish three inter-related cardinal results: optimal PDE regularity, exact controllability, and uniform stabilization. Thus, the paper takes a critical view on a spate of “abstract” results in “infinite-dimensional systems theory,” generated by unnecessarily complicated and highly limited “soft” methods, with no apparent awareness of the high degree of restriction of the abstract assumptions made—far from necessary—as well as on how to verify them in the case of multidimensional dynamical systems such as PDEs.

I. Lasiecka - One of the best experts on this subject based on the ideXlab platform.

  • l2 σ regularity of the Boundary to Boundary Operator b l for hyperbolic and petrowski pdes
    Abstract and Applied Analysis, 2003
    Co-Authors: I. Lasiecka, R. Triggiani
    Abstract:

    This paper takes up and thoroughly analyzes a technical mathematical issue in PDE theory, while—as a by-pass product—making a larger case. The technical issue is the L 2 ( Σ ) -regularity of the Boundary → Boundary Operator B ∗ L for (multidimensional) hyperbolic and Petrowski-type mixed PDEs problems, where L is the Boundary input → interior solution Operator and B is the control Operator from the Boundary. Both positive and negative classes of distinctive PDE illustrations are exhibited and proved. The larger case to be made is that hard analysis PDE energy methods are the tools of the trade—not soft analysis methods. This holds true not only to analyze B ∗ L , but also to establish three inter-related cardinal results: optimal PDE regularity, exact controllability, and uniform stabilization. Thus, the paper takes a critical view on a spate of “abstract” results in “infinite-dimensional systems theory,” generated by unnecessarily complicated and highly limited “soft” methods, with no apparent awareness of the high degree of restriction of the abstract assumptions made—far from necessary—as well as on how to verify them in the case of multidimensional dynamical systems such as PDEs.

  • L2(Σ)-regularity of the Boundary to Boundary Operator B∗L for hyperbolic and Petrowski PDEs
    Abstract and Applied Analysis, 2003
    Co-Authors: I. Lasiecka, R. Triggiani
    Abstract:

    This paper takes up and thoroughly analyzes a technical mathematical issue in PDE theory, while—as a by-pass product—making a larger case. The technical issue is the L 2 ( Σ ) -regularity of the Boundary → Boundary Operator B ∗ L for (multidimensional) hyperbolic and Petrowski-type mixed PDEs problems, where L is the Boundary input → interior solution Operator and B is the control Operator from the Boundary. Both positive and negative classes of distinctive PDE illustrations are exhibited and proved. The larger case to be made is that hard analysis PDE energy methods are the tools of the trade—not soft analysis methods. This holds true not only to analyze B ∗ L , but also to establish three inter-related cardinal results: optimal PDE regularity, exact controllability, and uniform stabilization. Thus, the paper takes a critical view on a spate of “abstract” results in “infinite-dimensional systems theory,” generated by unnecessarily complicated and highly limited “soft” methods, with no apparent awareness of the high degree of restriction of the abstract assumptions made—far from necessary—as well as on how to verify them in the case of multidimensional dynamical systems such as PDEs.

B. Kh. Turmetov - One of the best experts on this subject based on the ideXlab platform.

Khalid Latrach - One of the best experts on this subject based on the ideXlab platform.

  • Spectral analysis of monoenergetic transport equation with delayed neutrons in slab geometry
    ANNALI DELL'UNIVERSITA' DI FERRARA, 2020
    Co-Authors: Khalid Latrach, Najeh Salhi
    Abstract:

    In this paper, we give a general spectral analysis of the monoenergetic transport Operator with delayed neutrons and general Boundary where an abstract Boundary Operator relates the incoming and the outgoing fluxes in slab geometry. We discuss the asymptotic spectrum: the existence and nonexistence of eigenvalues in the half plane $$\big \{\lambda \in {\mathbb {C}}\, :\, \text {Re}\lambda >-\lambda ^{*} \big \}$$ { λ ∈ C : Re λ > - λ ∗ } where $$-\lambda ^{*}$$ - λ ∗ stands for the spectral bound of the streaming Operator. In particular, the strict monotonicity of a leading eigenvalue (when it exists) of the transport Operator with respect to different parameters of the equation is also discussed.

  • Time asymptotic behavior of the solution to the linear Boltzmann equation in finite bodies
    Afrika Matematika, 2020
    Co-Authors: Youssouf Kosad, Khalid Latrach
    Abstract:

    In this paper we discuss time asymptotic behavior of the solution to the Cauchy problem governed by the transport Operator in bounded geometry in the case where the Boundary conditions are dissipative and modeled by the bounce-back Boundary Operator plus a compact in $$L^1$$ L 1 -spaces. The case of multiplying compact Boundary Operator is considered in the last subsection.

  • Time asymptotic behaviour for linear transport equations with abstract Boundary conditions in slab geometry
    Transport Theory and Statistical Physics, 1994
    Co-Authors: Khalid Latrach
    Abstract:

    Abstract This paper is concerned with the large-time asymptotic behaviour of the solution to transport Cauchy problems in slab geometry with general Boundary Operators H relating the incoming and outgoing fluxes. It is composed of two parts. First, we consider the transport Cauchy problems with a general class of dissipative or conservative Boundary conditions (∥H∥ ≤ 1). In the second part, we treat the case of an arbitrary compact Boundary Operator H with no restriction on its norm. Our approach relies on the inverse Laplace transform and applies to dissipative as well as multiplying Boundary conditions.

Thomas Demeester - One of the best experts on this subject based on the ideXlab platform.

  • Construction of the Dirichlet to Neumann Boundary Operator for Triangles and Applications in the Analysis of Polygonal Conductors
    IEEE Transactions on Microwave Theory and Techniques, 2010
    Co-Authors: Thomas Demeester, D. De Zutter
    Abstract:

    This paper introduces a fast and accurate method to investigate the broadband inductive and resistive behavior of conductors with a nonrectangular cross section. The presented iterative combined waveguide mode (ICWM) algorithm leads to an expansion of the longitudinal electric field inside a triangle using a combination of parallel-plate waveguide modes in three directions, each perpendicular to one of the triangle sides. This expansion is used to calculate the triangle's Dirichlet to Neumann Boundary Operator. Subsequently, any polygonal conductor can be modeled as a combination of triangles. The method is especially useful to investigate current crowding effects near sharp conductor corners. In a number of numerical examples, the accuracy of the ICWM algorithm is investigated, and the method is applied to some polygonal conductor configurations.

  • Internal Impedance of Composite Conductors with Arbitrary Cross Section
    IEEE Transactions on Electromagnetic Compatibility, 2009
    Co-Authors: Thomas Demeester, D. De Zutter
    Abstract:

    A new way to calculate the internal inductance and resistance per unit length for an inhomogeneous conductor with arbitrary cross-sectional geometry is presented, based on the surface admittance Boundary Operator. The method is formulated in such a way, that the physical meaning of the internal impedance is clarified, as obtained by disregarding the external magnetic field. A comparison is made with the definitions known in literature to determine the internal impedance. In a number of numerical examples, the differences between those definitions are elucidated, and some physical properties of the internal impedance are investigated.

  • Applications of the Dirichlet-to-Neumann Boundary Operator in Transmission Line Modeling
    Electromagnetic Compatibility, 2009 20th International Zurich Symposium on, 2009
    Co-Authors: Thomas Demeester, Daniël De Zutter
    Abstract:

    The DtN Operator is a useful tool in the characterization of interconnect structures. In combination with the Method of Moments, it can be used for transmission line modeling or to directly determine the internal impedance of conductors. This paper presents a new calculation method for the Dirichlet-to-Neumann (DtN) Boundary Operator, in the important case of a rectangular block, based on the superposition of slab waveguide modes. Especially for its non-differential form, some numerical issues need to be addressed. It is further explained how the DtN Operator can be determined for composite blocks. The theory is illustrated by some numerical examples.

  • Quasi-TM Transmission Line Parameters of Coupled Lossy Lines Based on the Dirichlet to Neumann Boundary Operator
    Microwave Theory and Techniques, IEEE Transactions on, 2008
    Co-Authors: Thomas Demeester, Daniël De Zutter
    Abstract:

    This paper presents a new multiconductor transmission line model for general 2-D lossy configurations based on mode reciprocity. Particular attention is devoted to elucidate the validity of the quasi-TM model and the approximations that have to be invoked to obtain this model. A new derivation of the complex capacitance matrix is given, especially taking into account the presence of semiconductors. This derivation automatically leads to a nonclassical circuit signal current definition and demands for a formulation of the complex inductance problem consistent with that definition. The relevant resistance, inductance, conductance, and capacitance circuit matrices are obtained by solving Boundary integral equations only, making use of the Dirichlet to Neumann Boundary Operator for the different materials. This allows to simulate complex metal-insulator-semiconductor structures, as shown in the numerical examples.