scholarly journals When is a pseudo-differential equation solvable ?

2000 ◽  
Vol 50 (2) ◽  
pp. 443-460 ◽  
Author(s):  
Nicolas Lerner
Keyword(s):  
Differential Equation ◽  
Pseudo Differential Equation

ON THE CAUCHY PROBLEM FOR SOME PSEUDO-DIFFERENTIAL EQUATIONS OF SCHRÖDINGER TYPE

1996 ◽  
Vol 06 (03) ◽  
pp. 295-314 ◽  
Author(s):  
R. AGLIARDI ◽  
D. MARI
Keyword(s):  
Differential Equation ◽  
Cauchy Problem ◽  
Fundamental Solution ◽  
Differential Equations ◽  
Lower Order ◽  
Order Term ◽  
Well Posedness ◽  
Gevrey Spaces ◽  
The Cauchy Problem ◽  
Pseudo Differential Equation

A fundamental solution of the Cauchy problem is constructed for a pseudo-differential equation generalizing some Schrödinger equations. Then well-posedness of the Cauchy problem is proved in some Gevrey spaces whose indices depend on the lower order term of the operator.

scholarly journals APPLICATION OF p-ADIC ANALYSIS TO TIME SERIES

2013 ◽  
Vol 16 (04) ◽  
pp. 1350030 ◽  
Author(s):  
A. YU. KHRENNIKOV ◽  
S. V. KOZYREV ◽  
K. OLESCHKO ◽  
A. G. JARAMILLO ◽  
M. de JESÚS CORREA LÓPEZ
Keyword(s):  
Differential Equation ◽  
Time Series ◽  
Correlation Function ◽  
Punctuated Equilibrium ◽  
Oil Wells ◽  
Pseudo Differential Equation ◽  
Time Periods ◽  
Analysis Of Time Series

Time series defined by a p-adic pseudo-differential equation is investigated using the expansion of the time series over p-adic wavelets. Quadratic correlation function is computed. This correlation function shows a degree-like behavior and is locally constant for some time periods. It is natural to apply this kind of models for the investigation of avalanche processes and punctuated equilibrium as well as fractal-like analysis of time series generated by measurement of pressure in oil wells.

scholarly journals Modeling and simulation of fingering pattern formation in a combustion model

2015 ◽  
Vol 25 (04) ◽  
pp. 685-720 ◽  
Author(s):  
Lina Hu ◽  
Claude-Michel Brauner ◽  
Jie Shen ◽  
Gregory I. Sivashinsky
Keyword(s):  
Differential Equation ◽  
Pattern Formation ◽  
Nonlinear System ◽  
Boundary Conditions ◽  
Modeling And Simulation ◽  
Fourth Order ◽  
Combustion Model ◽  
Free Interface ◽  
Planar Front ◽  
Pseudo Differential Equation

We consider a model of gas–solid combustion with free interface proposed by L. Kagan and G. I. Sivashinsky. Our approach is twofold: (I) We eliminate the front and get to a fully nonlinear system with boundary conditions; (II) We use a fourth-order pseudo-differential equation for the front to achieve asymptotic regimes in rescaled variables. In both cases, we implement a numerical algorithm based on spectral method and represent numerically the evolution of the char. Fingering pattern formation occurs when the planar front is unstable. A series of simulations is presented to demonstrate the evolution of sparse fingers (I) and chaotic fingering (II).

scholarly journals Existence and Uniqueness for a Class of Stochastic Time Fractional Space Pseudo-Differential Equations

2016 ◽  
Vol 19 (1) ◽  
Author(s):  
Ke Hu ◽  
Niels Jacob ◽  
Chenggui Yuan
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Differential Equations ◽  
Existence And Uniqueness ◽  
Mild Solutions ◽  
Pseudo Differential Equation ◽  
Fractional Differential ◽  
Stochastic Fractional Differential Equations ◽  
Stochastic Time ◽  
Fractional Space

AbstractSome classes of stochastic fractional differential equations with respect to time and a pseudo-differential equation with respect to space are investigated. Using estimates for the Mittag-Leffler functions and a fixed point theorem, existence and uniqueness of mild solutions of the equations under consideration are established.

Pointwise Computation in an Ill-Posed Spherical Pseudo-Differential Equation

2015 ◽  
Vol 15 (2) ◽  
pp. 213-219 ◽  
Author(s):  
Sergei V. Pereverzyev ◽  
Pavlo Tkachenko
Keyword(s):  
Differential Equation ◽  
Least Squares ◽  
Hilbert Spaces ◽  
Least Squares Method ◽  
A Posteriori ◽  
Parameter Choice ◽  
Pseudo Differential Equation ◽  
A Posteriori Parameter Choice ◽  
Ill Posed ◽  
Numer Anal

AbstractIn the present paper, we consider the approximation of the solution of an ill-posed spherical pseudo-differential equation at a given point. While the methods for approximating the whole solution are well-studied in Hilbert spaces, such as the space of square-summable functions, the computation of values of the solution at given points is much less studied. This can be explained, in particular, by the fact that for square-summable functions the functional of pointwise evaluation is, in general, not well defined. To overcome this limitation we adjust the regularized least-squares method of An, Chen, Sloan and Womersley [Siam J. Numer. Anal. 50 (2012), no. 3, 1513–1534] by using a special a posteriori parameter choice rule. We also illustrate our theoretical findings by numerical results for the reconstruction of the solution at a given point.

scholarly journals On an equation being a fractional differential equation with respect to time and a pseudo-differential equation with respect to space related to Lévy-type processes

2012 ◽  
Vol 15 (1) ◽  
Author(s):  
Ke Hu ◽  
Niels Jacob ◽  
Chenggui Yuan
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Mild Solutions ◽  
Great Pleasure ◽  
Pseudo Differential Equation ◽  
Fractional Differential ◽  
Senior Colleague

AbstractIt is with great pleasure that we dedicate this paper to Professor Rudolf Gorenflo. In particular, the second named author wants to express his appreciation to an outstanding mathematician who was to him more than 30 years ago an inspiring teacher, and a very humane senior colleague later on.A class of fractional differential equations are investigated. Using estimates for Mittag-Leffler function and a fixed point theorem, we establish the existence and uniqueness of mild solutions of the equations.

Regularization by Aggregation of Global and Local Data on the Sphere

2016 ◽  
Vol 16 (2) ◽  
pp. 299-307 ◽  
Author(s):  
Pavlo Tkachenko
Keyword(s):  
Differential Equation ◽  
Linear Functional ◽  
Reproducing Kernel ◽  
Reproducing Kernel Hilbert Space ◽  
Local Data ◽  
Penalty Term ◽  
Functional Strategy ◽  
Pseudo Differential Equation ◽  
Ill Posed ◽  
Global And Local

AbstractIn the present paper we study how to combine a limited regional information with globally available noisy observations related to the quantity of interest through an ill-posed spherical pseudo-differential equation. We formulate such combination as a minimization problem involving two misfit terms and the penalty term in a reproducing kernel Hilbert space. Moreover, we illustrate the proposed scheme by a numerical example and discuss an aggregation of two approaches by a linear functional strategy for a better performance.

Sign in / Sign up

Export Citation Format

Share Document