A local in time existence and uniqueness result of an inverse problem for the Kelvin-Voigt fluids

2021 ◽  
Author(s):  
Pardeep Kumar ◽  
Kush Kinra ◽  
Manil T Mohan
Keyword(s):  
Inverse Problem ◽  
Existence And Uniqueness ◽  
Uniqueness Result ◽  
Time Existence

A GLOBAL IN TIME EXISTENCE AND UNIQUENESS RESULT FOR A SEMILINEAR INTEGRODIFFERENTIAL PARABOLIC INVERSE PROBLEM IN SOBOLEV SPACES

2007 ◽  
Vol 17 (04) ◽  
pp. 537-565 ◽  
Author(s):  
FABRIZIO COLOMBO ◽  
DAVIDE GUIDETTI
Keyword(s):  
Inverse Problem ◽  
Heat Conduction ◽  
Existence And Uniqueness ◽  
Parabolic Problem ◽  
Uniqueness Result ◽  
Convolution Kernel ◽  
Materials With Memory ◽  
Time Existence ◽  
With Memory ◽  
Abstract Existence

We prove a global in time abstract existence and uniqueness result for a general parabolic problem of reconstruction of a convolution kernel. The result is, in particular, applicable to the theory of heat conduction for materials with memory.

Stochastic non-resistive magnetohydrodynamic system with L\'{e}vy noise

2017 ◽  
Vol 25 (3) ◽  
Author(s):  
Utpal Manna ◽  
Manil T. Mohan ◽  
Sivaguru S. Sritharan
Keyword(s):  
Existence And Uniqueness ◽  
Uniqueness Result ◽  
Three Dimensions ◽  
Mhd Equations ◽  
Lévy Noise ◽  
Magnetohydrodynamic System ◽  
Levy Noise ◽  
Time Existence ◽  
Maximal Time ◽  
The Ideal

AbstractIn this work we prove the existence and uniqueness of path-wise solutions up to a maximal time for the viscous, non-resistive stochastic magnetohydrodynamic system perturbed by Lévy noise in two and three dimensions. The local-in-time existence and uniqueness result for the ideal and non-viscous MHD equations with Lévy noise is also addressed.

scholarly journals Existence and uniqueness results for an inverse problem for a semilinear equation with final overdetermination

Filomat ◽  
2018 ◽  
Vol 32 (3) ◽  
pp. 847-858 ◽  
Author(s):  
Ali Sazaklioglu ◽  
Abdullah Erdogan ◽  
Allaberen Ashyralyev
Keyword(s):  
Banach Space ◽  
Inverse Problem ◽  
Difference Scheme ◽  
Existence And Uniqueness ◽  
Uniqueness Result ◽  
Order Of Accuracy ◽  
First Order ◽  
Existence And Uniqueness Results ◽  
Semilinear Equation ◽  
Uniqueness Results

In the present paper, unique solvability of a source identification inverse problem for a semilinear equation with a final overdetermination in a Banach space is investigated. Moreover, the first order of accuracy Rothe difference scheme is presented for numerically solving this problem. The existence and uniqueness result for this difference scheme is given. The efficiency of the proposed method is evaluated by means of computational experiments.

ON THE TIME-DEPENDENT HARTREE–FOCK EQUATIONS COUPLED WITH A CLASSICAL NUCLEAR DYNAMICS

1999 ◽  
Vol 09 (07) ◽  
pp. 963-990 ◽  
Author(s):  
ERIC CANCÈS ◽  
CLAUDE LE BRIS
Keyword(s):  
Cauchy Problem ◽  
Fixed Point ◽  
Existence And Uniqueness ◽  
Uniqueness Result ◽  
Time Dependent ◽  
Nuclear Dynamics ◽  
Hartree Fock ◽  
Newtonian Dynamics ◽  
The Cauchy Problem ◽  
Time Existence

We prove a global-in-time existence and uniqueness result for the Cauchy problem in the setting of some model of Molecular Quantum Chemistry. The model we are concerned with consists of a coupling between the time-dependent Hartree–Fock equations (for the electrons) and the classical Newtonian dynamics (for the nuclei). The proof combines semigroup techniques and the Schauder fixed-point theorem. We also extend our result in order to treat the case of a molecule subjected to a time-dependent electric field.

Variational-hemivariational inverse problem for electro-elastic unilateral frictional contact problem

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Othmane Baiz ◽  
Hicham Benaissa ◽  
Zakaria Faiz ◽  
Driss El Moutawakil
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Contact Problem ◽  
Existence And Uniqueness ◽  
Frictional Contact ◽  
Hemivariational Inequalities ◽  
Frictional Contact Problem ◽  
Uniqueness Of A Solution

AbstractIn the present paper, we study inverse problems for a class of nonlinear hemivariational inequalities. We prove the existence and uniqueness of a solution to inverse problems. Finally, we introduce an inverse problem for an electro-elastic frictional contact problem to illustrate our results.

scholarly journals A Uniqueness Result for a Simple Superlinear Eigenvalue Problem

2021 ◽  
Vol 31 (2) ◽  
Author(s):  
Michael Herrmann ◽  
Karsten Matthies
Keyword(s):  
Eigenvalue Problem ◽  
Numerical Simulations ◽  
Convolution Operator ◽  
Existence And Uniqueness ◽  
Uniqueness Result ◽  
Constitutive Laws ◽  
Parameter Family ◽  
Shape Constraint ◽  
Special Case ◽  
Nonlinear Eigenfunctions

AbstractWe study the eigenvalue problem for a superlinear convolution operator in the special case of bilinear constitutive laws and establish the existence and uniqueness of a one-parameter family of nonlinear eigenfunctions under a topological shape constraint. Our proof uses a nonlinear change of scalar parameters and applies Krein–Rutman arguments to a linear substitute problem. We also present numerical simulations and discuss the asymptotics of two limiting cases.

scholarly journals Lorentz spaces in action on pressureless systems arising from models of collective behavior

2021 ◽  
Author(s):  
Raphaël Danchin ◽  
Piotr Bogusław Mucha ◽  
Patrick Tolksdorf
Keyword(s):  
Initial Data ◽  
Collective Behavior ◽  
Existence And Uniqueness ◽  
Maximal Regularity ◽  
Parabolic Systems ◽  
Lorentz Spaces ◽  
Regularity Estimate ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Time Existence

AbstractWe are concerned with global-in-time existence and uniqueness results for models of pressureless gases that come up in the description of phenomena in astrophysics or collective behavior. The initial data are rough: in particular, the density is only bounded. Our results are based on interpolation and parabolic maximal regularity, where Lorentz spaces play a key role. We establish a novel maximal regularity estimate for parabolic systems in $$L_{q,r}(0,T;L_p(\Omega ))$$ L q , r ( 0 , T ; L p ( Ω ) ) spaces.

scholarly journals On the differential system govering flows in magnetic field with data inLp

1998 ◽  
Vol 21 (2) ◽  
pp. 299-305 ◽  
Author(s):  
Fengxin Chen ◽  
Ping Wang ◽  
Chaoshun Qu
Keyword(s):  
Magnetic Field ◽  
Initial Data ◽  
Boundary Conditions ◽  
Differential System ◽  
Existence And Uniqueness ◽  
Mhd Equations ◽  
The Earth ◽  
Initial And Boundary Conditions ◽  
Time Existence ◽  
The Magnetic Field

In this paper we study the system governing flows in the magnetic field within the earth. The system is similar to the magnetohydrodynamic (MHD) equations. For initial data in spaceLp, we obtained the local in time existence and uniqueness ofweak solutions of the system subject to appropriate initial and boundary conditions.

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