Bifurcations of periodics from homoclinics in singular ODE: Applications to discretizations of travelling waves of PDE by Michael Feckan, Vassilios M. Rothos

“…Results are applied to discretization of travelling waves of certain p.d.e.…”
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Fireshape: a shape optimization toolbox for Firedrake by A. Paganini, F. Wechsung

Subjects: “…PDE-constrained Optimization…”
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Applications of Nijenhuis geometry III: Frobenius pencils and compatible non-homogeneous Poisson structures by Alexey Bolsinov, Andrey Konyaev, Vladimir Matveev

Subjects: “…Integrable PDE systems…”
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First heavenly partial differential equation: Mathematica file by Sobhi Berjawi

Subjects: “…partial differential equations (PDE)…”
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Linearly degenerate PDEs and quadratic line complexes by Evgeny Ferapontov, Jonathan Moss

Subjects: “…Multi-dimensional second order PDE…”
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Applications of Nijenhuis geometry IV: multicomponent KdV and Camassa-Holm equations by Alexey Bolsinov, Andrey Yu. Konyaev, Vladimir S. Matveev

Subjects: “…multicomponent integrable PDE systems…”
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An edge-based unstructured mesh discretisation in geospherical framework by Joanna Szmelter, Piotr K. Smolarkiewicz

Subjects: “…PDE on the sphere…”
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Mathematical modelling of the potential determinants of foot-and-mouth disease virus-induced death of bovine epithelial cells by Kyriaki Giorgakoudi

Subjects: “…PDE…”
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Unstructured mesh methods for stratified turbulent flows by Zhao Zhang

Subjects: “…Anelastic PDE…”
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Linear degeneracy in multidimensions by Jonathan Moss

“…Linear degeneracy of a PDE is a concept that is related to a number of interesting geometric constructions. …”
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Hydrodynamic reductions of multidimensional dispersionless PDEs: The test for integrability by Evgeny Ferapontov, Karima Khusnutdinova

“…A (d + 1)-dimensional dispersionless PDE is said to be integrable if its ncomponent hydrodynamic reductions are locally parametrized by (d − 1)n arbitrary functions of one variable. …”
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Periodic measures, transitions and exit times of stochastic differential equations by Johnny Zhong

“…Casting the time-periodic solution of the PDE as a fixed point problem and a convex optimisation problem, we give sufficient conditions in which the PDE is well-posed in a weak and classical sense. …”
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Applications of Nijenhuis geometry V: geodesic equivalence and finite-dimensional reductions of integrable quasilinear systems by Alexey Bolsinov, Andrey Yu. Konyaev, Vladimir S. Matveev

“…Next, we show that a certain evolutionary PDE system of hydrodynamic type constructed from L preserves the property of γ to be a g-geodesic. …”
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Design education: collaboration and cross-disciplinarity [front matter] by Erik Bohemia, Lyndon Buck, Kaare Eriksen, Ahmed Kovacevic, Nis Ovesen, Christian Tollestrup

“…The 18th International Conference on Engineering and Product Design Education (E&PDE) was held at the University of Aalborg on the 8th and 9th September 2016. …”
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Dispersionless integrable systems in 3D and Einstein-Weyl geometry by Evgeny Ferapontov, B. Kruglikov

“…For several classes of second order dispersionless PDEs, we show that the symbols of their formal linearizations define conformal structures which must be Einstein- Weyl in 3D (or self-dual in 4D) if and only if the PDE is integrable by the method of hydrodynamic reductions. …”
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Bayesian estimation and reconstruction of marine surface contaminant dispersion by Yang Liu, Christopher Harvey, Frederick Ellis Hamlyn, Cunjia Liu

“…We employ the fundamental convection-diffusion partial differential equation (PDE) to represent the general dispersion of a physical quantity in a non-uniform flow field. …”
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Physical properties of gravitational solitons by Salvatore Micciche

“…Soliton solutions of Einstein's field equations for space–times with two non-null, commuting Killing Vectors are exact solutions obtained using the solution-generating techniques that resemble the well-known Inverse Scattering Methods that have been widely used m the solution of certain nonlinear PDE's such as Korteweg–de Vries, Sine–Gordon, non-linear Schrödinger. …”
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Painleve equations and applications by Neil J. Southall

“…Any ODE with the Painlevé property is necessarily a reduction of an integrable PDE. Nevanlinna theory studies the value distribution and characterizes the growth of meromorphic functions, by using certain averaged properties on a disc of variable radius. …”
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On a class of integrable Hamiltonian equations in 2+1 dimensions by Ben Gormley, Evgeny Ferapontov, Vladimir Novikov

“…Based on the method of hydrodynamic reductions, the integrability conditions are derived (in the form of an involutive PDE system for the Hamiltonian density h). We show that the generic integrable density is expressed in terms of the Weierstrass σ-function: h(u, w) = σ(u)e w. …”
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Variational symmetries and pluri-Lagrangian structures for integrable hierarchies of PDEs by Matteo Petrera, Mats Vermeeren

“…We consider hierarchies of 2-dimensional Lagrangian PDEs (many of which have a natural $$(1\,{+}\,1)$$ ( 1 + 1 ) -dimensional space-time interpretation) and show that if the flow of each PDE is a variational symmetry of all others, then there exists a pluri-Lagrangian 2-form for the hierarchy. …”
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Hamiltonian structures for integrable hierarchies of Lagrangian PDEs by Mats Vermeeren

“…In the ODE (Lagrangian 1-form) case we discuss as examples the Toda hierarchy and the Kepler problem. As examples for the PDE (Lagrangian 2-form) case we present the potential and Schwarzian Korteweg-de Vries hierarchies, as well as the Boussinesq hierarchy.…”
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Finite-dimensional reductions and finite-gap-type solutions of multicomponent integrable PDEs by Alexey Bolsinov, Andrey Yu. Konyaev, Vladimir S. Matveev

“…We provide a link between solutions of our multicomponent PDE systems and solutions of this finite-dimensional system, and use it to construct animations of multicomponent analogous of soliton and cnoidal solutions.…”
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Second-order PDEs in 3D with Einstein-Weyl conformal structure by Sobhi Berjawi, Evgeny Ferapontov, Boris Kruglikov, Vladimir Novikov

“…A rigidity conjecture is proposed according to which for any generic second-order PDE with Einstein–Weyl property, all dependence on the 1-jet variables can be eliminated via a suitable contact transformation.…”
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Finite difference methods for solving mildly nonlinear elliptic partial differential equations by Jehad A.H. El-Nakla

“…By applying some well-known iterative methods, usually used to solve linear PDE systems, the thesis investigates their applicability to solve a set of four mildly nonlinear test problems. …”
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Second-order PDEs with integrable symbols by Sobhi Berjawi

“…The rigidity conjecture proposes that for any generic second-order PDE with Einstein–Weyl property, all dependence on the 1-jet variables can be eliminated via a suitable contact transformation. …”
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A mathematical model demonstrating the role of interstitial fluid flow on the clearance and accumulation of amyloid β in the brain by C.Y. Chen, Y.H. Tseng, John Ward

“…Asymptotic analysis is carried out for the steady states of the spatially homogeneous system in the vanishingly small limit of Aβ clearance rate. The PDE model is studied numerically for two cases, a spherically symmetric case and a more realistic 2D asymmetric case, allowing for nonuniform boundary conditions. …”
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A finite-volume module for simulating global all-scale atmospheric flows by Piotr K. Smolarkiewicz, Willem Deconinck, Mats Hamrud, Christian Kühnlein, George Mozdzynski, Joanna Szmelter, Nils P. Wedi

“…Furthermore, it employs semi-implicit forward-in-time integrators of the governing PDE systems, akin to but more general than those used in the NWP model. …”
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Mathematical modelling of magnesium corrosion for orthopaedic implants by Safia K. Ahmed

“…The backbone of this thesis is a PDE model for Mg corrosion, which considers distinct porous layers of \ce{Mg(OH)2} and \ce{MgCO3} surrounding a block of Mg with the advection and diffusion of \ce{H2O} and \ce{CO2} through porous media; this porous media assumption is a novel feature in comparison to other metal corrosion models. …”
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Development of a predictive mathematical model for coupled Stokes–Darcy flows in cross-flow membrane filtration by Navraj S. Hanspal, Atul N. Waghode, Vahid Nassehi, Richard J. Wakeman

“…Solutions to the system of partial differential equations (PDE’s) are obtained using the finite element method employing mixed interpolations for the primary field variables which are velocity and pressure. …”
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