Application de la théorie des fonctions convexes d'ordre supérieur à l'étude de certains procédés d'intégration numérique des équations différentielles
Application de la théorie des microfonctions holomorphes au problème de Cauchy à données singulières
Application des sentinelles à l'identification des pollutions dans une rivière
Application of a center manifold theory to a reaction-diffusion system of collective motion of camphor disks and boats
Unidirectional motion along an annular water channel can be observed in an experiment even with only one camphor disk or boat. Moreover, the collective motion of camphor disks or boats in the water channel exhibits a homogeneous and an inhomogeneous state, depending on the number of disks or boats, which looks like a kind of bifurcation phenomena. In a theoretical research, the unidirectional motion is represented by a traveling wave solution in a model. Hence it suffices to investigate a linearized...
Application of a noncompactness technique to an investigation of the existence of solutions to a nonlocal multivalued Darboux problem.
Application of bounded operators and Lyapunov's majorizing equations to the analysis of differential equations with a small parameter
Application of Calderón's inverse problem in civil engineering
In specific fields of research such as preservation of historical buildings, medical imaging, geophysics and others, it is of particular interest to perform only a non-intrusive boundary measurements. The idea is to obtain comprehensive information about the material properties inside the considered domain while keeping the test sample intact. This paper is focused on such problems, i.e. synthesizing a physical model of interest with a boundary inverse value technique. The forward model is represented...
Application of complex analysis to second order equations of mixed type
This paper deals with an application of complex analysis to second order equations of mixed type. We mainly discuss the discontinuous Poincaré boundary value problem for a second order linear equation of mixed (elliptic-hyperbolic) type, i.e. the generalized Lavrent’ev-Bitsadze equation with weak conditions, using the methods of complex analysis. We first give a representation of solutions for the above boundary value problem, and then give solvability conditions via the Fredholm theorem for integral...
Application of decomposition to hyperbolic, parabolic, and elliptic partial differential equations.
Application of He's homotopy perturbation method for Cauchy problem of ill-posed nonlinear diffusion equation.
Application of He's variational iteration method to solve semidifferential equations of th order.
Application of homogenization theory related to Stokes flow in porous media
We consider applications, illustration and concrete numerical treatments of some homogenization results on Stokes flow in porous media. In particular, we compute the global permeability tensor corresponding to an unidirectional array of circular fibers for several volume-fractions. A 3-dimensional problem is also considered.
Application of Interpolation Theory to the Analysis of the Convergence Rate for Finite Difference Schemes of Parabolic Type
Application of linear hyperbolic PDE to linear quantum fields in curved spacetimes : especially black holes, time machines and a new semi-local vacuum concept
Several situations of physical importance may be modelled by linear quantum fields propagating in fixed spacetime-dependent classical background fields. For example, the quantum Dirac field in a strong and/or time-dependent external electromagnetic field accounts for the creation of electron-positron pairs out of the vacuum. Also, the theory of linear quantum fields propagating on a given background curved spacetime is the appropriate framework for the derivation of black-hole evaporation (Hawking...
Application of Moser's method to a certain type of evolution equations
Application of relaxation scheme to degenerate variational inequalities
In this paper we are concerned with the solution of degenerate variational inequalities. To solve this problem numerically, we propose a numerical scheme which is based on the relaxation scheme using non-standard time discretization. The approximate solution on each time level is obtained in the iterative way by solving the corresponding elliptic variational inequalities. The convergence of the method is proved.
Application of restricted Backlund transformation to linearization of second order nonlinear parabolic equation
Application of Rothe's method to a parabolic inverse problem with nonlocal boundary condition
We consider an inverse problem for the determination of a purely time-dependent source in a semilinear parabolic equation with a nonlocal boundary condition. An approximation scheme for the solution together with the well-posedness of the problem with the initial value is presented by means of the Rothe time-discretization method. Further approximation scheme via Rothe’s method is constructed for the problem when and the integral kernel in the nonlocal boundary condition is symmetric.
Application of Rothe's method to abstract parabolic equations
Application of Rothe's method to parabolic variational inequalities