Generalizations of some classical inequalities and their applications
Generalizations of the Finite Element Method
This paper is concerned with the generalization of the finite element method via the use of non-polynomial enrichment functions. Several methods employ this general approach, e.g. the extended finite element method and the generalized finite element method. We review these approaches and interpret them in the more general framework of the partition of unity method. Here we focus on fundamental construction principles, approximation properties and stability of the respective numerical method. To...
Generalizations of the Lax-Milgram theorem.
Generalized analytic functions with applications to singular ordinary and partial differential equations [Book]
Generalized Backscattering and the Lax-Phillips Transform
2000 Mathematics Subject Classification: 35P25, 35R30, 58J50.Using the free-space translation representation (modified Radon transform) of Lax and Phillips in odd dimensions, it is shown that the generalized backscattering transform (so outgoing angle w = Sq in terms of the incoming angle with S orthogonal and Id-S invertible) may be further restricted to give an entire, globally Fredholm, operator on appropriate Sobolev spaces of potentials with compact support. As a corollary we show that the...
Generalized boundary value problems for nonlinear elliptic equations.
Generalized Cahn-Hilliard equations based on a microforce balance.
Generalized Cauchy problems for hyperbolic functional differential systems
A generalized Cauchy problem for hyperbolic functional differential systems is considered. The initial problem is transformed into a system of functional integral equations. The existence of solutions of this system is proved by using the method of successive approximations. Differentiability of solutions with respect to initial functions is proved. It is important that functional differential systems considered in this paper do not satisfy the Volterra condition.
Generalized characteristic equation of branching information measures.
Generalized characteristics uniqueness and regularity of solutions in a hyperbolic system of conservation laws
Generalized combined field integral equations for the iterative solution of the three-dimensional Helmholtz equation
This paper addresses the derivation of new second-kind Fredholm combined field integral equations for the Krylov iterative solution of tridimensional acoustic scattering problems by a smooth closed surface. These integral equations need the introduction of suitable tangential square-root operators to regularize the formulations. Existence and uniqueness occur for these formulations. They can be interpreted as generalizations of the well-known Brakhage-Werner [A. Brakhage and P. Werner, Arch....
Generalized Dirac Operators on Nonsmooth Manifolds and Maxwell's Equations.
Generalized dirichlet problem in nonlinear potential theory.
Generalized dissipativeness in a Banach space.
Generalized eigenfunctions of relativistic Schrödinger operators. I.
Generalized eigenfunctions of relativistic Schrödinger operators in two dimensions.
Generalized ellipsoidal and sphero-conal harmonics.
Generalized Fokker-Planck equations and convergence to their equilibria
We consider extensions of the classical Fokker-Planck equation uₜ + ℒu = ∇·(u∇V(x)) on with ℒ = -Δ and V(x) = 1/2|x|², where ℒ is a general operator describing the diffusion and V is a suitable potential.
Generalized Fokker-Planck theory for electron and photon transport in biological tissues: application to radiotherapy.
Generalized Fractional Evolution Equation
2000 Mathematics Subject Classification: Primary 46F25, 26A33; Secondary: 46G20In this paper we study the generalized Riemann-Liouville (resp. Caputo) time fractional evolution equation in infinite dimensions. We show that the explicit solution is given as the convolution between the initial condition and a generalized function related to the Mittag-Leffler function. The fundamental solution corresponding to the Riemann-Liouville time fractional evolution equation does not admit a probabilistic...