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[CT050]

Session Time & Room : 5D (Aug.25, 15:30-17:10) @G809
Type : Contributed Talk
Abstract : We address an inverse problem of recovering a space-dependent semilinear coefficient in the Cahn–Hilliard type system modeling tumor growth described by a system of partial differential equations with Dirichlet boundary condition using boundary-type measurement. First, we establish a new higher-order weighted Carleman estimate for the given system and then a suitable regularity of solutions for this nonlinear system is derived. Finally, we prove Lipschitz type stability for the tumor growth model.
Classification : 35R30, 35K15
Format : Talk at Waseda University
Author(s) :
- Barani Balan Natesan (Central University of Tamil Nadu)

Session Time & Room : 5D (Aug.25, 15:30-17:10) @G809
Type : Contributed Talk
Abstract : A multiscale mathematical model describing the metals biosorption on algal-bacterial photogranules within a sequencing batch reactor is presented. The model is based on systems of mixed PDEs on a spherical free boundary domain and IDEs derived from mass conservation principles. The model is integrated numerically to examine the role of the microbial species and EPS in the adsorption process, and the effect of metal concentration and biofilm adsorption properties on metal removal.
Classification : 35R35, 35L45, 92-10, 92B05
Format : Talk at Waseda University
Author(s) :
- Fabiana Russo (Temple University)
- Alberto Tenore (Department of Mathematics and Applications "R. Caccioppoli", University of Naples Federico II)
- Maria Rosaria Mattei (Department of Mathematics and Applications "R. Caccioppoli", University of Naples Federico II)
- Luigi Frunzo (Department of Mathematics and Applications "R. Caccioppoli", University of Naples Federico II)

Session Time & Room : 5D (Aug.25, 15:30-17:10) @G809
Type : Contributed Talk
Abstract : Membrane technology is one of the most promising engineering strategies for freshwater production and wastewater treatment. The major concern results in the formation of a fouling layer leading to increasing hydraulic resistance and flux decline during membrane operations. A one-dimensional continuous model has been developed by considering a free boundary value problem describing biofouling dynamics in membrane bioreactors. Numerical results demonstrated the model accuracy in predicting biofouling effects and the implications on process management.
Classification : 35R35, 35L45, 92-10, 92B05
Format : Talk at Waseda University
Author(s) :
- Vincenzo Luongo (University of Naples Federico II)
- Nicholas Cogan (Florida State University)

Session Time & Room : 5D (Aug.25, 15:30-17:10) @G809
Type : Contributed Talk
Abstract : Hybrid imaging techniques have been developed recently to produce clearer images than those produced by electrical impedance tomography. We focus on the inverse problem arising in the quantitative step of many hybrid imaging methods, formulated as recovering the isotropic conductivity of an object given internal current densities generated by applying different boundary conditions to the electrostatic equation. We provide a local Lipschitz stability for the general inverse problem in both full and partial data cases.
Classification : 35R30, 65N21, 92C55
Format : Talk at Waseda University
Author(s) :
- Lingyun Qiu (Yau Mathematical Sciences Center, Tsinghua University; Yanqi Lake Beijing Institute of Mathematical Sciences and Applications)
- Siqin Zheng (Yau Mathematical Sciences Center, Tsinghua University)

Session Time & Room : 5D (Aug.25, 15:30-17:10) @G809
Type : Contributed Talk
Abstract : In this talk, we establish the boundary stability result concerning the inverse source problem for a seventh-order Korteweg–de Vries (KdV) equation. Initially, we derive a new boundary Carleman estimate for the given system using the Dirichlet–Neumann type boundary conditions. We finally obtain a Lipschitz-type boundary stability estimate of a seventh-order KdV equation using the regularity results of the nonlinear KdV equation and the Bukhgeim-Klibanov method.
Classification : 35R30, 35Q53
Format : Online Talk on Zoom
Author(s) :
- Arivazhagan Anbu (SRM Institute of Science and Technology, Tiruchirappalli )
- Arivazhagan Anbu (Indian Institute of Technology Gandhinagar)