Construction of a unique mild solution of one-dimensional Keller-Segel systems with uniformly elliptic operators having variable coefficients

2018 ◽  
Vol 68 (4) ◽  
pp. 845-866
Author(s):  
Yumi Yahagi
Keyword(s):  
Mild Solution ◽  
Existence And Uniqueness ◽  
Local Existence ◽  
Variable Coefficients ◽  
Elliptic Operators ◽  
Successive Approximations ◽  
Main Method ◽  
One Dimensional ◽  
Local Existence And Uniqueness ◽  
Unique Mild Solution

Abstract A one-dimensional Keller-Segel system which is defined through uniformly elliptic operators having variable coefficients is considered. In the main theorems, the local existence and uniqueness of the mild solution of the system are proved. The main method to construct the mild solution is an argument of successive approximations by means of strongly continuous semi-groups.

AN INVERSE PROBLEM FOR THE HYPERBOLIC HEAT EQUATION

1992 ◽  
Vol 02 (01) ◽  
pp. 113-120
Author(s):  
E.G. SAVATEEV ◽  
L.M. DE SOCIO
Keyword(s):  
Inverse Problem ◽  
Heat Equation ◽  
Existence And Uniqueness ◽  
Local Existence ◽  
One Dimensional ◽  
Constructive Solution ◽  
Local Existence And Uniqueness ◽  
Diffusive Term ◽  
Hyperbolic Heat Equation

In this paper we prove a theorem of local existence and uniqueness for the solution of the hyperbolic heat equation in the case where the coefficient of the diffusive term is unknown. The problem is one-dimensional in space and the ratio of the two characteristics times, upon which the physics depends, is small. The demonstration relies on a constructive solution.

scholarly journals Local and Global Existence of Solution for Love Type Waves with Past History

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1998
Author(s):  
Mohamed Biomy ◽  
Khaled Zennir ◽  
Ahmed Himadan
Keyword(s):  
Existence And Uniqueness ◽  
Past History ◽  
Local Existence ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Linearization Method ◽  
Weak Compactness ◽  
Existence Of Solution ◽  
Local Existence And Uniqueness ◽  
Initial Boundary Value

In this paper, we consider an initial boundary value problem for nonlinear Love equation with infinite memory. By combining the linearization method, the Faedo–Galerkin method, and the weak compactness method, the local existence and uniqueness of weak solution is proved. Using the potential well method, it is shown that the solution for a class of Love-equation exists globally under some conditions on the initial datum and kernel function.

GENESIS OF A SOURCE/SINK LINE INTO A SINGULAR UPDRAFT

1998 ◽  
Vol 08 (03) ◽  
pp. 431-444 ◽  
Author(s):  
JOËL CHASKALOVIC
Keyword(s):  
Mathematical Models ◽  
Existence And Uniqueness ◽  
Vortex Line ◽  
Stokes Equations ◽  
Local Existence ◽  
Fluid Motion ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Local Existence And Uniqueness ◽  
Source Sink

Mathematical models applied to tornadoes describe these kinds of flows as an axisymmetric fluid motion which is restricted for not developing a source or a sink near the vortex line. Here, we propose the genesis of a family of a source/sink line into a singular updraft which can modeled one of the step of the genesis of a tornado. This model consists of a three-parameter family of fluid motions, satisfying the steady and incompressible Navier–Stokes equations, which vanish at the ground. We establish the local existence and uniqueness for these fields, at the neighborhood of a nonrotating singular updraft.

scholarly journals ROUGH VOLTERRA EQUATIONS 1: THE ALGEBRAIC INTEGRATION SETTING

2009 ◽  
Vol 09 (03) ◽  
pp. 437-477 ◽  
Author(s):  
AURÉLIEN DEYA ◽  
SAMY TINDEL
Keyword(s):  
Brownian Motion ◽  
Existence And Uniqueness ◽  
Local Existence ◽  
Volterra Equations ◽  
Existence And Uniqueness Theorem ◽  
Hölder Exponent ◽  
Local Existence And Uniqueness ◽  
Hurst Coefficient ◽  
Rough Path ◽  
Driving Signal

We define and solve Volterra equations driven by an irregular signal, by means of a variant of the rough path theory called algebraic integration. In the Young case, that is for a driving signal with Hölder exponent γ > 1/2, we obtain a global solution, and are able to handle the case of a singular Volterra coefficient. In case of a driving signal with Hölder exponent 1/3 < γ < 1/2, we get a local existence and uniqueness theorem. The results are easily applied to the fractional Brownian motion with Hurst coefficient H > 1/3.

Sign in / Sign up

Export Citation Format

Share Document