scholarly journals On an existence and uniqueness theory for nonlinear differential-algebraic equations

1991 ◽  
Vol 10 (3) ◽  
pp. 343-359 ◽  
Author(s):  
Sebastian Reich
Keyword(s):  
Existence And Uniqueness ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Uniqueness Theory

scholarly journals Linear differential algebraic equations with constant coefficients

1970 ◽  
Vol 4 (2) ◽  
pp. 28-35 ◽  
Author(s):  
M Sahadet Hossain ◽  
M Mostafizur Rahman
Keyword(s):  
Existence And Uniqueness ◽  
Differential Algebraic Equations ◽  
Canonical Forms ◽  
Algebraic Equations ◽  
Numerical Examples ◽  
Constant Coefficients ◽  
Dae Systems ◽  
International University ◽  
Linear Differential ◽  
Modern Mathematics

Differential-algebraic equations (DAEs) arise in a variety of applications. Their analysis and numerical treatment, therefore, plays an important role in modern mathematics. The paper gives an introduction to the topics of DAEs. Examples of DAEs are considered showing their importance for practical problems. Some essential concepts that are really essential for understanding the DAE systems are introduced. The canonical forms of DAEs are discussed widely to make them more efficient and easy for practical use. Also some numerical examples are discussed to clarify the existence and uniqueness of the system's solutions. Keywords: differential-algebraic equations, index concept, canonical forms. DOI: 10.3329/diujst.v4i2.4365 Daffodil International University Journal of Science and Technology Vol.4(2) 2009 pp.28-35

Operator Differential-Algebraic Equations Arising in Fluid Dynamics

2013 ◽  
Vol 13 (4) ◽  
pp. 443-470 ◽  
Author(s):  
Etienne Emmrich ◽  
Volker Mehrmann
Keyword(s):  
Existence And Uniqueness ◽  
Differential Algebraic Equations ◽  
Generalized Solutions ◽  
Operator Matrix ◽  
Algebraic Equations ◽  
Infinite Dimensions ◽  
Initial Value ◽  
Block Operator ◽  
Oseen Problem ◽  
Problem Data

Abstract. Existence and uniqueness of generalized solutions to initial value problems for a class of abstract differential-algebraic equations (DAEs) is shown. The class of equations covers, in particular, the Stokes and Oseen problem describing the motion of an incompressible or nearly incompressible Newtonian fluid but also their spatial semi-discretization. The equations are governed by a block operator matrix with entries that fulfill suitable inf-sup conditions. The problem data are required to satisfy appropriate consistency conditions. The results in infinite dimensions are compared in detail with those known for the DAEs that arise after semi-discretization in space. Explicit solution formulas are derived in both cases.

scholarly journals On the Existence and Uniqueness of the Solution of Linear Fractional Differential-Algebraic System

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Zaiyong Feng ◽  
Ning Chen
Keyword(s):  
Existence And Uniqueness ◽  
Fractional Derivatives ◽  
Differential Algebraic Equations ◽  
Equivalent Transformation ◽  
Algebraic Equations ◽  
Differential Algebraic System ◽  
Uniqueness Of The Solution ◽  
Fractional Differential ◽  
Matrix Pair ◽  
Kronecker Canonical Form

The existence and uniqueness of the solution of a new kind of system—linear fractional differential-algebraic equations (LFDAE)—are investigated. Fractional derivatives involved are under the Caputo definition. By using the tool of matrix pair, the LFDAE in which coefficients matrices are both square matrices have unique solution under the condition that coefficients matrices make up a regular matrix pair. With the help of equivalent transformation and Kronecker canonical form of the coefficients matrices, the sufficient condition for existence and uniqueness of the solution of the LFDAE in which coefficients matrices are both not square matrices is proposed later. Two examples are given to justify the obtained theorems in the end.

scholarly journals Condensed Forms for Linear Port-Hamiltonian Descriptor Systems

2019 ◽  
Vol 35 ◽  
pp. 65-89 ◽  
Author(s):  
Lena Scholz
Keyword(s):  
Dynamical Systems ◽  
Existence And Uniqueness ◽  
Hamiltonian Formulation ◽  
Differential Algebraic Equations ◽  
Descriptor Systems ◽  
Constant Rank ◽  
Algebraic Equations ◽  
Uniqueness Of Solutions ◽  
Structure Preserving ◽  
Strangeness Index

Motivated by the structure which arises in the port-Hamiltonian formulation of constraint dynamical systems, structure preserving condensed forms for skew-adjoint differential-algebraic equations (DAEs) are derived. Moreover, structure preserving condensed forms under constant rank assumptions for linear port-Hamiltonian differential-algebraic equations are developed. These condensed forms allow for the further analysis of the properties of port-Hamiltonian DAEs and to study, e.g., existence and uniqueness of solutions or to determine the index. It can be shown that under certain conditions for regular port-Hamiltonian DAEs the strangeness index is bounded by $\mu\leq1$.

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