Search results for "Mathematical analysis"
showing 10 items of 2409 documents
A free boundary problem stemmed from combustion theory. Part II: Stability, instability and bifurcation results
2002
AbstractWe deal with a free boundary problem, depending on a real parameter λ, in a infinite strip in R2, providing stability, instability and bifurcation.
A note on the analytic solutions of the Camassa-Holm equation
2005
Abstract In this Note we are concerned with the well-posedness of the Camassa–Holm equation in analytic function spaces. Using the Abstract Cauchy–Kowalewski Theorem we prove that the Camassa–Holm equation admits, locally in time, a unique analytic solution. Moreover, if the initial data is real analytic, belongs to H s ( R ) with s > 3 / 2 , ‖ u 0 ‖ L 1 ∞ and u 0 − u 0 x x does not change sign, we prove that the solution stays analytic globally in time. To cite this article: M.C. Lombardo et al., C. R. Acad. Sci. Paris, Ser. I 341 (2005).
On superconvergence techniques
1987
A brief survey with a bibliography of superconvergence phenomena in finding a numerical solution of differential and integral equations is presented. A particular emphasis is laid on superconvergent schemes for elliptic problems in the plane employing the finite element method.
Milton’s conjecture on the regularity of solutions to isotropic equations
2003
Abstract We present examples showing that the threshold for the integrability of the gradient of solutions to isotropic equations is 2K/(K−1). The main tools are p-laminates and Beltrami Operators.
Removability of a Level Set for Solutions of Quasilinear Equations
2005
In this paper, we study the removability of a level set for the solutions of quasilinear elliptic and parabolic equations of the second order. We show, under rather general assumptions on the coeff...
Walsh function analysis of 2-D generalized continuous systems
1990
The importance of the generalized or singular 2D continuous systems are demonstrated by showing their use in the solution of partial differential equations in two variables. A technique is presented for solving these systems in terms of Walsh functions. The method replaces the solution of a two-variable partial differential equation with the solution of a linear algebraic generalized 2D Sylvester equation. An efficient technique for the recursive solution of the latter equation is offered. All the results apply also in the usual Roesser 2D state-space case. >
An algorithmic construction of entropies in higher-order nonlinear PDEs
2006
A new approach to the construction of entropies and entropy productions for a large class of nonlinear evolutionary PDEs of even order in one space dimension is presented. The task of proving entropy dissipation is reformulated as a decision problem for polynomial systems. The method is successfully applied to the porous medium equation, the thin film equation and the quantum drift–diffusion model. In all cases, an infinite number of entropy functionals together with the associated entropy productions is derived. Our technique can be extended to higher-order entropies, containing derivatives of the solution, and to several space dimensions. Furthermore, logarithmic Sobolev inequalities can …
Smoothed Particle ElectroMagnetics: A mesh-free solver for transients
2006
AbstractIn this paper an advanced mesh-free particle method for electromagnetic transient analysis, is presented. The aim is to obtain efficient simulations by avoiding the use of a mesh such as in the most popular grid-based numerical methods. The basic idea is to obtain numerical solutions for partial differential equations describing the electromagnetic problem by using a set of particles arbitrarily placed in the problem domain. The mesh-free smoothed particle hydrodynamics method has been adopted to obtain numerical solution of time domain Maxwell's curl equations. An explicit finite difference scheme has been employed for time integration. Details about the numerical treatment of elec…
Numerical experiments with single mode gyrotron equations
2012
Gyrotrons are microwave sources whose operation is based on the stimulated cyclotron radiation of electrons oscillating in a static magnetic field. This process is described by the system of two complex differential equations: nonlinear first order ordinary differential equation with parameter (averaged equation of electron motion) and second order partial differential equation for high frequency field (RF field) in resonator (Schrödinger type equation for the wave amplitude). The stationary problem of the single mode gyrotron equation in short time interval with real initial conditions was numerically examined in our earlier work. In this paper we consider the stationary and nonstationary …
Calculation of heat and moisture distribution in the porous media layer
2007
In this paper we study the problem of the diffusion of one substance through the pores of a porous material which may absorb and immobilize some of the diffusing substances with the evolution or absorption of heat. The transfer of moisture and the heat are described by the model. The system of two partial differential equations (PDEs) is derived, one equation expresses the rate of change of concentration of water vapour in the air spaces and the other the rate of change of temperature. The obtained initial‐boundary value problem is approximated by using the finite volume method. This procedure allows us to reduce the 2D transfer problem described by a system of PDEs to initial value problem…