### Research seminars

Research seminars consist of an approximately one-hour long talk, given by team member or a guest, followed by 30 min discussion on the presented topic. They are part of the Research seminar for Differential Equations and Numerical Analysis held at the Faculty of Science, Department of Mathematics.

# Research seminar "Modeling and computations of self-propelled elastic cylindrical micro-swimmers​"

On Friday, June 17, 2016, Prof. Annalisa Quaini from the University of Houston (USA), gave a talk on Modeling and computations of self-propelled elastic cylindrical micro-swimmers​ at the Research seminar for differential equations and numerical analysis.
Abstract of the talk can be found here.

# Research seminar "Generalised solutions for fully nonlinear systems of PDE & vectorial Calculus of Variations in $L^\infty$"

On Monday, May 16, 2016, Prof. Nikos Katzourakis from the University of Reading (UK), gave a talk on Generalised solutions for fully nonlinear systems of PDE & vectorial Calculus of Variations in $L^\infty$​ at the Research seminar for differential equations and numerical analysis.
Abstract of the talk can be found here.

# Research seminar "On a family of fourth-order diffusion equations"

On Monday, April 4, 2016, Dr. Mario Bukal, project member from the UniZG FER, gave a talk on A family of fourth-order diffusion equations at the Research seminar for differential equations and numerical analysis.
Abstract of the talk (in Croatian) can be found here.

# Research seminar "Yudovich theorem"

On Monday, March 14, 2016, Prof. Tomasz Cieslak from the Institute of Mathematics of Polish Academy of Sciences, Warsaw (Poland), gave a talk on Yudovich theorem at the Research seminar for differential equations and numerical analysis.
Abstract of the talk can be found here.

# Research seminar "Discrete geometric conservation law and nonlinear stability on a moving domain"

On February 29, 2016, Marija Galić, mag. math. (PhD student at the project) gave a talk at the Research seminar for differential equations and numerical analysis.

TitleDiscrete geometric conservation law and nonlinear stability on a moving domain

# Research seminar "Convergence analysis of the kinematically coupled scheme and its extensions for the fluid-structure interaction"

On January 11, 2016, Dr. Boris Muha gave a talk at the Research seminar for differential equations and numerical analysis.

Title: Convergence analysis of the kinematically coupled scheme and its extensions for the fluid-structure interaction

Abstract (in Croatian) can be found here.

# Research seminar "Some remarks about intrinsically strained plates in nonlinear elasticity"

On Monday, June 8, 2015, Prof. Peter Hornung from TU Dresden (Germany) gave a talk at the Research seminar for differential equations and numerical analysis.

TitleSome remarks about intrinsically strained plates in nonlinear elasticity.

# Research seminar "Non-periodic homogenization and dimensional reduction in elasticity on the example of the bending rod"

On Monday, February 23rd, 2015, the talk at the Research seminar for Differential Equations and Numerical Analysis was held by dr.sc. Igor Velčić.

TitleNon-periodic homogenization and dimensional reduction in elasticity on the example of the bending rod

Abstract (in Croatian): Diskutirat ćemo izvedbu ”bending modela” štapa Gamma konvergencijom uzimajući u obzir i moguće oscilacije materijala ne pretpostavljajući nikakvu posebnu pravilnost u oscilacijama. Seminar se temelji na zajedničkom radu s M. Marohnićem.

# Research seminar "Mathematical analysis of island formation in epitaxially strained crystalline films"

On Monday, February 9th, 2015, the talk at the Research seminar for Differential Equations and Numerical Analysis was held by Barbara Zwicknagl, Ph.D. (Universität Bonn).

TitleMathematical analysis of island formation in epitaxially strained crystalline films.

Abstract: I will discuss analytical results on variational models that have been introduced in the physical literature to describe the shapes of epitaxially strained crystalline films deposited on rigid substrates, when there is a mismatch between the lattice parameters of the two crystals. The driving energy functional accounts for the elastic energy stored in the film due to a crystallographic misfit, and the surface energy of the film’s free surface. We discuss existence of optimal film profiles and some geometric properties of minimizers if they exist. The influence of a non-vanishing miscut angle is also considered. This talk is based on joint works with P. Bella and M. Goldman, and with I. Fonseca and A. Pratelli.

# Research seminar "On asymptotic nonlinear stability of stationary solutions to Stefan problem"

On Thursday, December 18th, 2014, Mahir Hadžić, Ph.D. (King's College London) gave the talk at the Research seminar for Differential Equations and Numerical Analysis entiteled "On asymptotic nonlinear stability of stationary solutions to Stefan problem".

# Public presentation of the research project "Mathematical Analysis of Multi-physics Problems Involving Thin and Composite Structures and Fluids" (MAMPITCoStruFl)

Public presentation of the installation research project "Mathematical Analysis of Multi-physics Problems Involving Thin and Composite Structures and Fluids" (MAMPITCoStruFl), funded by the Croatian Science Foundation, to scientific community took place on Wednesday, December 17th, 2014 at the Faculty of Science University of Zagreb. The presentation was given by the principal investigator Igor Velčić, and team members Maroje Marohnić and Boris Muha. The invitation to the presentation can be found here.

# Research seminar "Existence of a weak solution to a fluid-structure interaction problem with Navier slip boundary condition - part II"

On MondayNovember 242014doc.dr.sc. Boris Muha (UniZg-PMF) gave the second part of the talk entiteled "Existence of a weak solution to a fluid-structure interaction problem with Navier slip boundary condition - part II" at the Research seminar for Differential Equations and Numerical Analysis.

# Research seminar "Existence of a weak solution to a fluid-structure interaction problem with Navier slip boundary condition - part I"

On Monday, November 10, 2014, doc.dr.sc. Boris Muha (UniZg-PMF) gave a talk at the Research seminar for Differential Equations and Numerical Analysis entiteled "Existence of a weak solution to a fluid-structure interaction problem with Navier slip boundary condition - part I".

Abstract (in Croatian): U ovom predavanju formulirat ćemo problem slobodne granice koji opisuje interakciju viskoznog, inkompresibilnog fluida sa linearno elastičnom Koiterovom ljuskom. Tok fluida opisan je inkompresibilnim Navier-Stokesovim jednadžbama, a sustav je spojen preko Navierovih slip rubnih uvjeta za brzinu fluida. Taj tip rubnih uvjeta dobro opisuje mnoge fizikalne situacije. U kontekstu interakcije fluida i čvrstih tijela posebno je interesantan zbog toga što omogućuje modeliranje kontakta izmedu čvrstih tijela, te tako zaobilazi paradokse vezane uz kontakt i klasične no-slip rubne uvjete. Dokazat ćemo egzistenciju slabog rješenja promatranog problema. Izložen dokaz je konstruktivan i temelji se na semidiskretizaciji i metodi razdvajanja operatora (operator splitting).