Existence, uniqueness and regularity of piezoelectric partial differential equations

References

• Feldmann N, Schulze V, Claes L, et al. Inverse piezoelectric material parameter characterization using a single disc-shaped specimen. tm – Technisches Messen. 1 Sep 2020;87(s1):s50–s55.
   Google Scholar
• Feldmann N, Jurgelucks B, Claes L, et al. A sensitivity-based optimisation procedure for the characterisation of piezoelectric discs. Proc Meet Acoust. 2019;38(1):030004.
   Google Scholar
• Jurgelucks B, Claes L, Walther A, et al. Optimization of triple-ring electrodes on piezoceramic transducers using algorithmic differentiation. Optim Methods Softw. 2018;33:1–21.
   Web of Science ®Google Scholar
• Birman V. Thermal effects on measurements of dynamic processes in composite structures using piezoelectric sensors. Smart Mater Struct. 1996 Aug;5(4):379–385.
   Google Scholar
• Damjanovic D. Hysteresis in piezoelectric and ferroelectric materials; 2006. Chapter 4, p. 337–465.
   Google Scholar
• Smith RC. Smart material systems : model development. Philadelphia,PA: SIAM; 2005.
   Google Scholar
• Nicaise S, Mercier D. Existence, uniqueness, and regularity results for piezoelectric systems. SIAM J Math Anal. 2005;37:651–672.
   Web of Science ®Google Scholar
• Imperiale S, Joly P. Mathematical and numerical modelling of piezoelectric sensors. ESAIM: Math Model Numer Anal – Modélisation Mathématique Et Analyse Numérique. 2012;46(4):875–909.
   Web of Science ®Google Scholar
• Leugering G, Novotny A, Menzala G, et al. Shape sensitivity analysis of a quasi-electrostatic piezoelectric system in multilayered media. Math Methods Appl Sci. 2010;33(17):2118–2131.
   Web of Science ®Google Scholar
• Kaltenbacher M. Numerical simulation of mechatronic sensors and actuators: finite elements for computational multiphysics. 3rd ed., Berlin Heidelberg: Springer; 2015.
   Google Scholar
• Lahmer T. Forward and inverse problems in piezoelectricity [dissertation]. University of Erlangen-Nuremberg; 2008.
   Google Scholar
• Kaltenbacher B, Lahmer T, Mohr M, et al. PDE based determination of piezoelectric material tensors. Eur J Appl Math. 2006;17(4):383–416.
   Google Scholar
• Cardone G, Nazarov S, Sokolowski J. Topological derivatives in piezoelectricity. Technical Report 35, IECN. 2008.
   Google Scholar
• Nicaise S. Stability and controllability of the elecromagneto-elastic system. Portugaliae Math Nova Srie. 2003;01:60.
   Google Scholar
• Nakamura G, Akamatsu M. Well-posedness of initial-boundary value problems for piezoelectric equations. Appl Anal. 2002;81(1):129–141.
   Google Scholar
• Antil H, Brown T, Sayas FJ. A problem in control of elastodynamics with piezoelectric effects. IMA Journal of Numerical Analysis. 2019;12:2839–2870.
   Google Scholar
• Melnik V. Existence and uniqueness theorems of the generalized solution for a class of non-stationary problems of coupled electroelasticity. S Math (iz. Vuz). 1991;35:24–32.
   Google Scholar
• Miara B. Contrlabilit d'un corps pizolectrique. C R De L'Acadmie Des Sci – Ser I – Math. 2001;333(3):267–270.
   Google Scholar
• Jurgelucks B. Increased sensitivity in parameter identification problems for piezoelectrics [dissertation]. Paderborn University; 2019.
   Google Scholar
• Dineva P, Gross D, Müller R, et al. Piezoelectric materials. In: Dynamic fracture of piezoelectric materials. Springer; 2014. p. 7–32.
   Google Scholar
• Evans L. Partial differential equations. American Mathematical Society; 1998. (Graduate studies in mathematics; Vol. 19).
   Google Scholar
• Ding Z. A proof of the trace theorem of sobolev spaces on Lipschitz domains. Proc Am Math Soc. 1996;124(2):591–600.
   Web of Science ®Google Scholar
• Adams R, Fournier J. Sobolev spaces. Elsevier Science; 2003. (Pure and Applied Mathematics).
   Google Scholar
• Schweizer B. Partielle Differentialgleichungen: Eine anwendungsorientierte Einführung. Berlin,Heidelberg, Germany: Springer-Verlag; 2013.
   Google Scholar
• Wloka J. Partial differential equations. Cambridge, United Kingdom: Cambridge University Press; 1987.
   Google Scholar
• Stein E. Singular integrals and differentiability properties of functions (pms-30). Princeton, New Jersey: Princeton University Press; 2016.
   Google Scholar
• Larsson S, Thomée V. Partial differential equations with numerical methods. Berlin,Heidelberg, Germany: Springer Science & Business Media; 2008.
   Google Scholar
• Alnæs M, Blechta J, Hake J, et al. The fenics project version 1.5. Archive Numer Softw. 2015;3(100):9–23.
   Google Scholar