Formulation of the Problem of Stability. Global Uniqueness of Solutions. Stiffness of Shells. Well-Posedness Classes

2008 ◽  
pp. 263-295
Keyword(s):  
Well Posedness ◽  
Uniqueness Of Solutions ◽  
Global Uniqueness

scholarly journals Several Fixed-Point Theorems for F -Contractions in Complete Branciari b -Metric Spaces and Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Lili Chen ◽  
Shuai Huang ◽  
Chaobo Li ◽  
Yanfeng Zhao
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Related Result ◽  
Fixed Point Problem ◽  
Common Fixed Points ◽  
Point Problem ◽  
Well Posedness ◽  
Uniqueness Of Solutions

In this paper, we prove the existence and uniqueness of fixed points for F -contractions in complete Branciari b -metric spaces. Furthermore, an example for supporting the related result is shown. We also present the concept of the weak well-posedness of the fixed-point problem of the mapping T and discuss the weak well-posedness of the fixed-point problem of an F -contraction in complete Branciari b -metric spaces. Besides, we investigate the problem of common fixed points for F -contractions in above spaces. As an application, we apply our main results to solving the existence and uniqueness of solutions for a class of the integral equation and the dynamic programming problem, respectively.

Well-posedness of Stratonovich multi-valued SDEs driven by semimartingales

2014 ◽  
Vol 14 (04) ◽  
pp. 1450005
Author(s):  
Jing Wu
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Existence And Uniqueness ◽  
Uniqueness Result ◽  
Time Change ◽  
Random Time ◽  
Approximation Technique ◽  
Well Posedness ◽  
Uniqueness Of Solutions ◽  
Random Time Change

In this paper we consider Stratonovich type multi-valued stochastic differential equations (MSDEs) driven by general semimartingales. Based on an existence and uniqueness result for MSDEs with respect to continuous semimartingales, we apply the random time change and approximation technique to prove existence and uniqueness of solutions to Stratonovich type multi-valued SDEs driven by general semimartingales with summable jumps.

scholarly journals Well-Posedness and Exponential Estimates for the Solutions to Neutral Stochastic Functional Differential Equations with Infinite Delay

2020 ◽  
Vol 8 (5) ◽  
pp. 434-446
Author(s):  
Hussein K. Asker
Keyword(s):  
Differential Equations ◽  
Infinite Delay ◽  
Functional Differential Equations ◽  
Well Posedness ◽  
Stochastic Functional Differential Equations ◽  
Uniqueness Of Solutions ◽  
Exponential Estimates ◽  
Global Condition ◽  
Functional Differential ◽  
Stochastic Functional

AbstractIn this work, neutral stochastic functional differential equations with infinite delay (NSFD-EwID) have been addressed. By using the Euler-Maruyama scheme and a localization argument, the existence and uniqueness of solutions to NSFDEwID at the state space Cr under the local weak monotone condition, the weak coercivity condition and the global condition on the neutral term have been investigated. In addition, the L2 and exponential estimates of NSFDEwID have been studied.

scholarly journals Well-posedness of evolutionary Navier-Stokes equations with forces of low regularity on two-dimensional domains

2021 ◽  
Author(s):  
Karl Kunisch ◽  
Eduardo Renteria Casas
Keyword(s):  
Stokes Equation ◽  
Existence And Uniqueness ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Well Posedness ◽  
Uniqueness Of Solutions ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Arbitrary Dimensions ◽  
Parameter Ranges

Existence and uniqueness of solutions to the Navier-Stokes equation in dimension two with forces in the space $L^q( (0,T); \bWmop)$ for $p$ and $q$ in  appropriate parameter ranges are proven. The case of spatially measured-valued inhomogeneities is included. For the associated Stokes equation the well-posedness results are verified in arbitrary dimensions with $1 < p, q < \infty$ arbitrary.

scholarly journals On some Inverse Parabolic Problems with Pointwise Overdetermination

2001 ◽  
Vol 14 (4) ◽  
pp. 463-474
Author(s):  
Sergey G. Pyatkov ◽  
Keyword(s):  
Inverse Problems ◽  
Sobolev Spaces ◽  
Parabolic System ◽  
Existence And Uniqueness ◽  
Parabolic Problems ◽  
Well Posedness ◽  
Sobolev Classes ◽  
Uniqueness Of Solutions

We examine well-posedness questions in the Sobolev spaces of inverse problems of recovering coefficients depending on time in a parabolic system. The overdetermination conditions are values of a solution at some collection of points lying inside the domain and on its boundary. The conditions obtained ensure existence and uniqueness of solutions to these problems in the Sobolev classes

scholarly journals Well-Posedness of Reset Control Systems as State-Dependent Impulsive Dynamical Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Alfonso Baños ◽  
Juan I. Mulero
Keyword(s):  
Control Systems ◽  
Dynamic Systems ◽  
Well Posedness ◽  
Sufficient Condition ◽  
Uniqueness Of Solutions ◽  
State Dependent ◽  
Starting Point ◽  
Definition Of ◽  
Reset Control ◽  
Well Posed

Reset control systems are a special type of state-dependent impulsive dynamic systems, in which the time evolution depends both on continuous dynamics between resets and the discrete dynamics corresponding to the resetting times. This work is devoted to investigate well-posedness of reset control systems, taking as starting point the classical definition of Clegg and Horowitz. Well-posedness is related to the existence and uniqueness of solutions, and in particular to the resetting times to be well defined and distinct. A sufficient condition is developed for a reset system to have well-posed resetting times, which is also a sufficient condition for avoiding Zeno solutions and, thus, for a reset control system to be well-posed.

A historical survey of some mathematical aspects of Newtonian fluid flows

2001 ◽  
Vol 54 (6) ◽  
pp. 525-562 ◽  
Author(s):  
RKh Zeytounian
Keyword(s):  
Fluid Dynamics ◽  
Newtonian Fluid ◽  
Existence And Uniqueness ◽  
Fluid Flows ◽  
Well Posedness ◽  
Kinetic Theory Of Gases ◽  
Historical Survey ◽  
Uniqueness Of Solutions ◽  
Fluid Dynamics Equations ◽  
Dynamics Problems

This article deals with a survey of the Newtonian fluid dynamics equations with some historical notes and a discussion related to the solvability of fluid flows problems. On the way, we discuss briefly various questions related with the behavior of fluid flows governed by these fluid dynamics equations. Some of these questions are, in fact, closely connected with the well-posedness of fluid dynamics problems. We touch on the problem of the fluid dynamics limit of the Boltzmann equation of the kinetic theory of gases. An overview of some rigorous recent results on the existence and uniqueness of solutions of the fluid flows problems concludes this paper. At the end, after some concluding remarks, there are 306 references.

scholarly journals On the well-posedness of the anisotropically-reduced two-dimensional Kuramoto-Sivashinsky Equation

2022 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
David Massatt
Keyword(s):  
Initial Data ◽  
Global Existence ◽  
Existence And Uniqueness ◽  
Well Posedness ◽  
Two Dimensional ◽  
Periodic Domain ◽  
Uniqueness Of Solutions ◽  
Global Existence And Uniqueness ◽  
Sivashinsky Equation

<p style='text-indent:20px;'>We address the global existence and uniqueness of solutions for the anisotropically reduced 2D Kuramoto-Sivashinsky equations in a periodic domain with initial data <inline-formula><tex-math id="M1">\begin{document}$ u_{01} \in L^2 $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M2">\begin{document}$ u_{02} \in H^{-1 + \eta} $\end{document}</tex-math></inline-formula> for <inline-formula><tex-math id="M3">\begin{document}$ \eta &gt; 0 $\end{document}</tex-math></inline-formula>.</p>

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