Page 460 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 460
NALYSIS, CONTROL AND INVERSE PROBLEMS FOR PARTIAL DIFFERENTIAL
EQUATIONS (MS-22)
Strong unique continuation at the boundary in linear elasticity and its
connection with optimal stability in the determination of unknown
boundaries
Edi Rosset, rossedi@units.it
Università di Trieste, Italy
Coauthors: Giovanni Alessandrini, Antonino Morassi, Sergio Vessella
Quantitative estimates of Strong Unique Continuation at the boundary for solutions to the
isotropic Kirchhoff-Love plates subject to Dirichlet conditions, and for solutions to the Gen-
eralized plane stress problem subject to Neumann conditions are presented. These results have
been applied to prove optimal stability estimates for the inverse problem of determining un-
known boundaries.
References
[1] G. Alessandrini, E. Rosset, S. Vessella, Optimal three spheres inequality at the boundary
for the Kirchhoff-Love plate’s equation with Dirichlet conditions, Arch. Rational Mech.
Anal., 231 (2019), 1455–1486.
[2] A. Morassi, E. Rosset, S. Vessella, Optimal stability in the identification of a rigid inclu-
sion in an isotropic Kirchhoff-Love plate, SIAM J. Math. Anal., 51 (2019), 731–747.
[3] A. Morassi, E. Rosset, S. Vessella, Optimal identification of a cavity in the Generalized
Plane Stress problem in linear elasticity, J. Eur. Math. Soc., to appear.
[4] A. Morassi, E. Rosset, S. Vessella, Doubling Inequality at the Boundary for the Kirchhoff-
Love Plate’s Equation with Dirichlet Conditions, Le Matematiche, LXXV (2020), 27–55,
Open access.
Weak Solutions for an Implicit, Degenerate Poro-elastic Plate System
Justin Webster, websterj@umbc.edu
University of Maryland, Baltimore County, United States
Coauthor: Elena Gurvich
We consider a recent plate model obtained as a scaled limit of the three dimensional quasi-static
Biot system of poro-elasticity. The result is a “2.5" dimensional linear system that couples
traditional Euler-Bernoulli plate dynamics to a pressure equation in three dimensions, where
diffusion acts only transversely. Motived by application, we allow the permeability function to
be time-dependent, making the problem non-autonomous and disqualifying much of the stan-
dard theory. Weak solutions are defined and the problem is framed abstractly as an implicit,
degenerate evolution problem:
[Bp]t + A(t)p = S.
Existence is obtained, and uniqueness follows under additional hypotheses on the temporal
regularity of the permeability. Time permitting, we address the inertial case with constant per-
meability by way of semigroup theory.
458
EQUATIONS (MS-22)
Strong unique continuation at the boundary in linear elasticity and its
connection with optimal stability in the determination of unknown
boundaries
Edi Rosset, rossedi@units.it
Università di Trieste, Italy
Coauthors: Giovanni Alessandrini, Antonino Morassi, Sergio Vessella
Quantitative estimates of Strong Unique Continuation at the boundary for solutions to the
isotropic Kirchhoff-Love plates subject to Dirichlet conditions, and for solutions to the Gen-
eralized plane stress problem subject to Neumann conditions are presented. These results have
been applied to prove optimal stability estimates for the inverse problem of determining un-
known boundaries.
References
[1] G. Alessandrini, E. Rosset, S. Vessella, Optimal three spheres inequality at the boundary
for the Kirchhoff-Love plate’s equation with Dirichlet conditions, Arch. Rational Mech.
Anal., 231 (2019), 1455–1486.
[2] A. Morassi, E. Rosset, S. Vessella, Optimal stability in the identification of a rigid inclu-
sion in an isotropic Kirchhoff-Love plate, SIAM J. Math. Anal., 51 (2019), 731–747.
[3] A. Morassi, E. Rosset, S. Vessella, Optimal identification of a cavity in the Generalized
Plane Stress problem in linear elasticity, J. Eur. Math. Soc., to appear.
[4] A. Morassi, E. Rosset, S. Vessella, Doubling Inequality at the Boundary for the Kirchhoff-
Love Plate’s Equation with Dirichlet Conditions, Le Matematiche, LXXV (2020), 27–55,
Open access.
Weak Solutions for an Implicit, Degenerate Poro-elastic Plate System
Justin Webster, websterj@umbc.edu
University of Maryland, Baltimore County, United States
Coauthor: Elena Gurvich
We consider a recent plate model obtained as a scaled limit of the three dimensional quasi-static
Biot system of poro-elasticity. The result is a “2.5" dimensional linear system that couples
traditional Euler-Bernoulli plate dynamics to a pressure equation in three dimensions, where
diffusion acts only transversely. Motived by application, we allow the permeability function to
be time-dependent, making the problem non-autonomous and disqualifying much of the stan-
dard theory. Weak solutions are defined and the problem is framed abstractly as an implicit,
degenerate evolution problem:
[Bp]t + A(t)p = S.
Existence is obtained, and uniqueness follows under additional hypotheses on the temporal
regularity of the permeability. Time permitting, we address the inertial case with constant per-
meability by way of semigroup theory.
458
