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CLASSICAL solutions OF HYPERBOLIC INITIAL boundary-value problems WITH STATE-DEPENDENT DELAYS

NONLINEAR OSCILLATIONS 2011年第4期13卷 595-612页

作者： Czernous, W. Univ Gdansk Inst Math PL-80952 Gdansk Poland

We consider the initial boundary-value problem for a system of quasilinear partial functional differential equations of the first order partial derivative(t)z(i)(t, x) + Sigma(n)(j=1) rho(ij)(t, x, V(z;t, x))partial derivative(xj)z(i)(t, x) = G(i)(t, x, V(z;t, x)), 1 <= i <= m, where V is a nonlinear operator of the Volterra type that maps bounded (with respect to seminorm) subsets of the space of Lipschitz continuously differentiable functions into bounded subsets of this space. Using the method of bicharacteristics and a fixed-point theorem, we prove the local existence, uniqueness, and continuous dependence on data of classical solutions of the problem. This approach covers systems of the form partial derivative(t)z(i)(t, x) + Sigma(n)(j=1) rho(ij)(t, x, z(psi(t, x, z(t, x))))partial derivative(xj)z(i)(t, x) = G(i)(t, x, z(psi(t, x, z(t, x)))), 1 <= i <= m, where (t, x) bar right arrow z((t, x)) is the Hale operator, and all components of psi may depend on. (t, x, z((t, x))). More specifically, problems with deviating arguments and integro-differential systems are included.

关键词： EXPONENTIAL functions boundary value problems -- numerical solutions NONLINEAR operators INTEGRO-differential equations FUNCTIONAL differential equations MATHEMATICAL analysis MAPPINGS (Mathematics)

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Bifurcation of solutions of singular Fredholm boundary value problems

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DIFFERENTIAL EQUATIONS 2011年第4期47卷 453-461页

作者： Boichuk, A. A. Shegda, L. M. Natl Acad Sci Inst Math Kiev Ukraine Ivano Frankivsk Natl Tech Univ Oil & Gas Ivano Frankivsk Ukraine

We obtain conditions for the bifurcation of solutions of linear singular Fredholm boundary value problems with a small parameter under the assumption that the unperturbed singular differential system can be reduced to central canonical form. Using the Vishik-Lyusternik method and the technique of Moore-Penrose pseudoinverse matrices, we suggest an algorithm for finding a family of linearly independent solutions of such boundary value problems for the general case in which the number of boundary conditions specified by a linear vector functional does not coincide with the number of unknowns in the singular differential system.

关键词： BIFURCATION theory FREDHOLM equations boundary value problems -- numerical solutions PSEUDOINVERSES VECTOR spaces MATHEMATICAL optimization

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Analysis of Sandwich Beams With a Compliant Core and With In-Plane Rigidity-Extended High-Order Sandwich Panel Theory Versus Elasticity

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JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME 2012年第4期79卷 41001-41001页

作者： Phan, Catherine N. Frostig, Yeoshua Kardomateas, George A. Georgia Inst Technol Sch Aerosp Engn Atlanta GA 30332 USA Technion Israel Inst Technol Fac Civil & Environm Engn Dept Struct Engn & Construct Management IL-32000 Haifa Israel

A new one-dimensional high-order theory for orthotropic elastic sandwich beams is formulated. This new theory is an extension of the high-order sandwich panel theory (HSAPT) and includes the in-plane rigidity of the core. In this theory, in which the compressibility of the soft core in the transverse direction is also considered, the displacement field of the core has the same functional structure as in the high-order sandwich panel theory. Hence, the transverse displacement in the core is of second order in the transverse coordinate and the in-plane displacements are of third order in the transverse coordinate. The novelty of this theory is that it allows for three generalized coordinates in the core (the axial and transverse displacements at the centroid of the core and the rotation at the centroid of the core) instead of just one (midpoint transverse displacement) commonly adopted in other available theories. It is proven, by comparison to the elasticity solution, that this approach results in superior accuracy, especially for the cases of stiffer cores, for which cases the other available sandwich computational models cannot predict correctly the stress fields involved. Thus, this theory, referred to as the "extended high-order sandwich panel theory" (EHSAPT), can be used with any combinations of core and face sheets and not only the very "soft" cores that the other theories demand. The theory is derived so that all core/face sheet displacement continuity conditions are fulfilled. The governing equations as well as the boundary conditions are derived via a variational principle. The solution procedure is outlined and numerical results for the simply supported case of transverse distributed loading are produced for several typical sandwich configurations. These results are compared with the corresponding ones from the elasticity solution. Furthermore, the results using the classical sandwich model without shear, the first-order shear, and the earlier HSAPT are al

关键词： SANDWICH construction (Materials) RIGIDITY (Geometry) ELASTICITY ORTHOTROPY (Mechanics) MATERIALS -- Compression testing COORDINATES STIFFNESS (Mechanics) VARIATIONAL principles boundary value problems -- numerical solutions

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Minimal and maximal solutions to second-order boundary value problems with state-dependent deviating arguments

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BULLETIN OF THE LONDON MATHEMATICAL SOCIETY 2011年第1期43卷 164-174页

作者： Figueroa, Ruben Lopez Pouso, Rodrigo Univ Santiago de Compostela Dept Math Anal Fac Math Santiago De Compostela 15782 Spain

We prove the existence of solutions between given lower and upper solutions for second-order boundary value problems with deviating arguments, and we show that the set of those solutions has minimal and maximal elements, but not necessarily a least or a greatest one. We consider deviating functions which depend on the unknown solution and its derivative. Some sufficient conditions for having lower and upper solutions are also provided.

关键词： boundary value problems -- numerical solutions MAXIMAL functions EXISTENCE theorems DEVIATION (Statistics) INTERVAL analysis (Mathematics) MATHEMATICAL analysis

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Axisymmetric solutions to Time-Fractional Heat Conduction Equation in a Half-Space under Robin boundary Conditions

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INTERNATIONAL JOURNAL OF DIFFERENTIAL EQUATIONS 2012年第unknown期2012卷 1-13页

作者： Povstenko, Y. Z. Jan Dlugosz Univ Inst Math & Comp Sci PL-42200 Czestochowa Poland European Univ Informat & Econ EWSIE Dept Comp Sci PL-03741 Warsaw Poland

The time-fractional heat conduction equation with the Caputo derivative of the order 0 < alpha < 2 is considered in a half-space in axisymmetric case under two types of Robin boundary condition: the mathematical one with the prescribed linear combination of the values of temperature and the values of its normal derivative and the physical condition with the prescribed linear combination of the values of temperature and the values of the heat flux at the boundary.

关键词： SYMMETRY (Mathematics) HEAT equation boundary value problems -- numerical solutions HEAT conduction CAPUTO fractional derivatives MATHEMATICAL analysis COMBINATIONS (Mathematics) HEAT flux TEMPERATURE measurements

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The aero-acoustic resonance behavior of partially covered slender cavities

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EXPERIMENTS IN FLUIDS 2011年第5期51卷 1353-1367页

作者： de Jong, Arjen Teake Bijl, Hester Scarano, Fulvio Delft Univ Technol NL-2611 HS Delft Netherlands

The present investigation focuses on the aeroacoustic resonance of cavities with a width much larger than their length or depth and partially covered, as often encountered in automotive door gaps. The cavities are under influence of a low Mach number flow with a relatively thick boundary layer. Under certain conditions, these cavities can acoustically resonate with the flow. The upstream and downstream edge of the opening as well as the cover lip overhang location and boundary layer thickness are parametrically varied in an experimental campaign, and the effect of the parameters on the resonance amplitude is investigated. Slender rectangular cavity geometries with an opening length of 8 mm and spanwise width of 500 mm are used. The cavity flow-induced acoustic response is measured with pressure transducers at different spanwise locations inside the cavity. Hot-wire measurements are performed to quantify the boundary layer characteristics. Furthermore, high-speed time-resolved particle image velocimetry is used to capture the instantaneous velocity field around the opening geometries. When the boundary layer thickness is increased, the cavity resonance amplitude diminishes. The cover lip overhang location has a large influence on the resonance response, which can be attributed to changes in the cavity driven flow properties. Rounding of the upstream edge promotes resonance, whereas rounding of the downstream edge can diminish it. A possible explanation of the phenomenon is given on the basis of the PIV observations.

关键词： boundary value problems -- numerical solutions TRANSDUCERS ACOUSTIC emission FLUID dynamics SPEED

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A new Legendre wavelet operational matrix of derivative and its applications in solving the singular ordinary differential equations

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JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS 2011年第8期348卷 1787-1796页

作者： Mohammadi, F. Hosseini, M. M. Yazd Univ Fac Math Yazd Iran

In the present paper, a new Legendre wavelet operational matrix of derivative is presented. Shifted Legendre polynomials and their properties are employed for deriving a general procedure for forming this matrix. The application of the proposed operational matrix for solving initial and boundary value problems is explained. Then the scheme is tested for linear and nonlinear singular examples. The obtained results demonstrate efficiency and capability of the proposed method. (C) 2011 Published by Elsevier Ltd. on behalf of The Franklin Institute.

关键词： DIFFERENTIAL equations -- numerical solutions MATRICES WAVELETS (Mathematics) LEGENDRE'S polynomials boundary value problems -- numerical solutions NONLINEAR theories MATHEMATICAL analysis

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On the Global Relation and the Dirichlet-to-Neumann Correspondence

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STUDIES IN APPLIED MATHEMATICS 2011年第1期126卷 75-102页

作者： Dassios, G. Doschoris, M. Univ Patras Dept Chem Engn Div Appl Math GR-26504 Patras Greece

The recently developed Fokas method for solving two-dimensional boundary value problems (BVP) via the use of global relations is utilized to solve axisymmetric problems in three dimensions. In particular, novel integral representations for the interior and exterior Dirichlet and Neumann problems for the sphere are derived, which recover and improve the already known solutions of these problems. The BVPs considered in this paper can be classically solved using either the finite Legendre transform or the Mellin-sine transform (which can be derived from the classical Mellin transform in a way similar to the way that the sine transform can be derived from the Fourier transform). The Legendre transform representation is uniformly convergent at the boundary, but it involves a series that is not useful for many applications. The Mellin-sine transform involves of course an integral but it is not uniformly convergent at the boundary. In this paper: (a) The Legendre transform representation is rederived in a simpler approach using algebraic manipulations instead of solving ODEs. (b) An integral representation, different that the Mellin-sine transform representation is derived which is uniformly convergent at the boundary. Furthermore, the derivation of the Fokas approach involves only algebraic manipulations, instead of solving an ordinary differential equation.

关键词： NEUMANN problem RELATION algebras DIRICHLET problem boundary value problems -- numerical solutions DIFFERENTIAL equations -- numerical solutions MELLIN transform STOCHASTIC convergence

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Axisymmetrical boundary-value problems of elasticity theory for finite-length cylinders and cones

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DOKLADY PHYSICS 2011年第7期56卷 407-412页

作者： Popov, G. Ya. Mechnikov Natl Univ UA-65082 Odessa Ukraine

The article presents the solution for boundary-value problems of the elasticity theory of finite-length cylinders and cones to satisfy its axisymmetrical deformation. It says that the integral transform is applied to get the exact solution of boundary-value problem for cylinder torsion and torsion deformation of cone. It mentions that the subsequent use of inversion formulas gives the precise solutions for cylinder and the sliding-seal condition must be fulfilled to find the solution for cone.

关键词： boundary value problems -- numerical solutions CYLINDERS (Engines) CONES DEFORMATIONS (Mechanics) INTEGRAL transforms INVERSIONS (Geometry)

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Infinitely many solutions for an elliptic Neumann problem involving critical Sobolev growth

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JOURNAL OF DIFFERENTIAL EQUATIONS 2011年第6期251卷 1389-1414页

作者： Cao, Daomin Yan, Shusen Chinese Acad Sci AMSS Inst Appl Math Beijing 100190 Peoples R China Cent China Normal Univ Sch Math & Stat Wuhan 430079 Peoples R China Univ New England Dept Math Sch Sci & Technol Armidale NSW 2351 Australia

In this paper, we prove the existence of infinitely many solutions for the following elliptic problem with critical Sobolev growth: -Delta u = vertical bar u vertical bar(2)*(-2)u + g(u) in Omega, partial derivative u/partial derivative nu = 0 on partial derivative Omega, where Omega is a bounded domain in R-N with C-3 boundary, N >= 3, nu is the outward unit normal of partial derivative Omega, 2* = 2N/N-2, and g(t) = mu vertical bar t vertical bar(p-2)t - t, or g(t) = mu t, where p is an element of (2, 2*), mu > 0 are constants. We obtain the existence of infinitely many solutions under certain assumptions on N, p and partial derivative Omega. In particular, if g(t) = mu t with mu > 0, N >= 7, and Omega is a strictly convex domain, then the problem has infinitely many solutions. (C) 2011 Published by Elsevier Inc.

关键词： NEUMANN problem PROBLEM solving EXISTENCE theorems CONVEX domains MATHEMATICAL constants boundary value problems -- numerical solutions

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