A sufficient condition for the well posedness of a Goursat problem
Alpha Well-Posedness, Alpha Stability, and the Matrix Theorems of H.-O. Kreiss.
Applications of Lie Group Analysis to Mathematical Modelling in Natural Sciences
Today engineering and science researchers routinely confront problems in mathematical modeling involving solutions techniques for differential equations. Sometimes these solutions can be obtained analytically by numerous traditional ad hoc methods appropriate for integrating particular types of equations. More often, however, the solutions cannot be obtained by these methods, in spite of the fact that, e.g. over 400 types of integrable second-order ordinary differential equations were summarized...
Baroclinic Kelvin Waves in a Rotating Circular Basin
A linear, uniformly stratified ocean model is used to investigate propagation of baroclinic Kelvin waves in a cylindrical basin. It is found that smaller wave amplitudes are inherent to higher mode individual terms of the obtained solutions that are also evanescent away of a costal line toward the center of the circular basin. It is also shown that the individual terms if the obtained solutions can be visualized as spinning patterns in rotating stratified fluid confined in a circular basin. Moreover,...
Boundary value problems for linear partial differential equation with constant coefficients. Non-homogeneous equation in the halfplane
Diffusion phenomenon for second order linear evolution equations
We present an abstract theory of the diffusion phenomenon for second order linear evolution equations in a Hilbert space. To derive the diffusion phenomenon, a new device developed in Ikehata-Matsuyama [5] is applied. Several applications to damped linear wave equations in unbounded domains are also given.
Extension of formal power series solutions
Generalized Gevrey classes and multi-quasi-hyperbolic operators.
Incompressible inviscid limit for the full magnetohydrodynamic flows on expanding domains
In this paper we study the incompressible inviscid limit of the full magnetohydrodynamic flows on expanding domains with general initial data. By applying the relative energy method and carrying out detailed analysis on the oscillation part of the velocity, we prove rigorously that the gradient part of the weak solutions of the full magnetohydrodynamic flows converges to the strong solution of the incompressible Euler system in the whole space, as the Mach number, viscosity as well as the heat conductivity...
Inhomogeneous Gevrey ultradistributions and Cauchy problem
-oценки решения задачи Коши для одномерного гиперболического уравнения высокого порядка с постоянными коэффициентами
Local solvability for semilinear partial differential equations of constant strength.
Nash equilibria for a model of traffic flow with several groups of drivers
Traffic flow is modeled by a conservation law describing the density of cars. It is assumed that each driver chooses his own departure time in order to minimize the sum of a departure and an arrival cost. There are N groups of drivers, The i-th group consists of κi drivers, sharing the same departure and arrival costs ϕi(t),ψi(t). For any given population sizes κ1,...,κn, we prove the existence of a Nash equilibrium solution, where no driver can lower his own total cost by choosing a different departure...
On Lp - Lp' Estimates for the Wave Equation.
On the Davey-Stewartson systems
On the hyperbolicity of a third order operator and the generalized Goursat-Darboux problem
On the Operator Solutions of Difference Equations
On the radius of spatial analyticity for the higher order nonlinear dispersive equation
In this work, using bilinear estimates in Bourgain type spaces, we prove the local existence of a solution to a higher order nonlinear dispersive equation on the line for analytic initial data . The analytic initial data can be extended as holomorphic functions in a strip around the -axis. By Gevrey approximate conservation law, we prove the existence of the global solutions, which improve earlier results of Z. Zhang, Z. Liu, M. Sun, S. Li, (2019).
Resolución del problema de Cauchy para ecuaciones en derivadas parciales totalmente hiperbólicas.
The Cauchy problem for coupled Yang-Mills and scalar fields in the Lorentz gauge