TY - GEN
T1 - On higher index differential-algebraic equations in infinite dimensions
AU - Trostorff, Sascha
AU - Waurick, Marcus
PY - 2018/4/28
Y1 - 2018/4/28
N2 - We consider initial value problems for differential-algebraic equations in a possibly infinite-dimensional Hilbert space. Assuming a growth condition for the associated operator pencil, we prove existence and uniqueness of solutions for arbitrary initial values in a distributional sense. Moreover, we construct a nested sequence of subspaces for initial values in order to obtain classical solutions.
AB - We consider initial value problems for differential-algebraic equations in a possibly infinite-dimensional Hilbert space. Assuming a growth condition for the associated operator pencil, we prove existence and uniqueness of solutions for arbitrary initial values in a distributional sense. Moreover, we construct a nested sequence of subspaces for initial values in order to obtain classical solutions.
KW - differential-algebraic equations
KW - higher index
KW - infinite-dimensional state space
KW - consistent initial values
KW - distributional solutions
KW - Hilbert space
UR - https://arxiv.org/abs/1710.08750
UR - https://www.springer.com/us/book/9783319759951
U2 - 10.1007/978-3-319-75996-8_27
DO - 10.1007/978-3-319-75996-8_27
M3 - Conference contribution book
SN - 9783319759951
VL - 268
T3 - Operator Theory: Advances and Applications
SP - 477
EP - 486
BT - The Diversity and Beauty of Applied Operator Theory
A2 - Böttcher, Albrecht
A2 - Potts, Daniel
A2 - Stollmann, Peter
A2 - Wenzel, David
PB - Springer
CY - Cham, Switzerland
T2 - International Workshop on Operator Theory and its Applications
Y2 - 14 August 2017 through 18 August 2017
ER -