Colloquium, Gianne Derks
Plats: Zoom, https://lu-se.zoom.us/j/67556376164
Kontakt: mikael [dot] persson_sundqvist [at] math [dot] lth [dot] se
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Title: Existence and stability of fronts in inhomogeneous wave equations
Speaker: Gianne Derks, Professor at University of Surrey, UK, and Hedda Andersson guest professor.
Abstract: Models describing waves in anisotropic media or media with imperfections usually have inhomogeneous terms. Examples of such models can be found in many applications, for example in nonlinear optical waveguides, water waves moving over a bottom with topology, currents in nonuniform Josephson junctions, DNA-RNAP interactions etc. Homogeneous nonlinear wave equations are Hamiltonian partial differential equations with the homogeneity providing an extra symmetry in the form of the spatial translations. Inhomogeneities break the translational symmetry, though the Hamiltonian structure is still present. When the spatial translational symmetry is broken, travelling waves are no longer natural solutions. Instead, the travelling waves tend to interact with the inhomogeneity and get trapped, reflected, or slowed down.
In this talk, wave equations with finite length inhomogeneities will be considered, assuming that the spatial domain can be written as the union of disjoint intervals, such that on each interval the wave equation is homogeneous. The underlying Hamiltonian structure allows for a rich family of stationary front solutions and the values of the energy (Hamiltonian) in each intermediate interval provide natural parameters for the family of orbits. Criteria for the existence of and stability of stationary solutions will be discussed. The results will be illustrated with an example related to a Josephson junction system with a finite length inhomogeneity associated with variations in the Josephson tunnelling critical current and an application to DNA-RNAP interactions.
Zoom link: https://lu-se.zoom.us/j/67556376164