Guide Partial Differential Equations and Applications

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Numerical methods for time-dependent partial differential equations, hyperbolic conservation laws, degenerate parabolic equations, numerical analysis, scientific computing. Numerical ordinary differential equations, numerical linear algebra, dynamical systems, inverse problems.


  1. Differential Equations & Applications.
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Convex analysis, convex optimization, monotone operators, computational data science, applied nonlinear analysis. Optimal control and inverse problems for partial differential equations, control of Navier-Stokes equations, numerical partial differential equations, nonlinear semigroup theory, dynamical systems in Banach spaces, stochastic differential equations and applications, applied functional analysis.

About this Research Topic

Numerical analysis and scientific computing; numerical methods for partial differential equations involving free boundary and moving interface problems, and problems on irregular domains, finite difference and finite element methods; CFD, and biological flows. Dynamical systems generated by ordinary, delay, and partial differential equations; stability, bifurcation, singular perturbation.


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  • Nonlinear ordinary differential equations, semi- linear parabolic and elliptic partial differential equations. Nonlinear PDEs, optimal control problems and differential Games, nonsmooth analysis and geometric measure theory. Geometric singular perturbation theory, existence and stability of traveling waves. Numerical analysis of partial differential equations and scientific computation with applications to fluid flows and wave propagation, including acoustics, electromagnetism, optics, and plasma.

    Ele-Math – Differential Equations & Applications

    Inverse problems, including active control of sound and radar imaging. Programs M. Ordinary Differential Equations, Partial Differential Equations and Analysis Faculty conduct research on theoretical and numerical issues for a variety of partial differential equations: semilinear parabolic equations including semigroup theory, elliptic equations, hyperbolic systems including systems of conservation laws, and dispersive equations. Lorena Bociu Associate Professor Partial Differential Equations: qualitative and quantitative properties of solutions to systems of PDEs, as well as associated stabilization and controllability issues.

    Stephen Campbell Distinguished Professor Implicit systems of ordinary differential equations, including numerical algorithms and control; applications to constrained mechanical systems, optimal control, and failure detection.

    Courses & Units

    Alina Chertock Professor, Associate Director for CRSC, Department Head Numerical methods for time-dependent partial differential equations, hyperbolic conservation laws, degenerate parabolic equations, numerical analysis, scientific computing. Moody Chu Professor Numerical ordinary differential equations, numerical linear algebra, dynamical systems, inverse problems.

    Control of partial differential equations and applications

    Patrick Combettes Distinguished Professor Convex analysis, convex optimization, monotone operators, computational data science, applied nonlinear analysis. Kazufumi Ito Professor Optimal control and inverse problems for partial differential equations, control of Navier-Stokes equations, numerical partial differential equations, nonlinear semigroup theory, dynamical systems in Banach spaces, stochastic differential equations and applications, applied functional analysis. Recently, new scenarios for transition have been proposed that are based on the non-normality of the linearized operator.

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    • Citations Publications citing this paper. Sensitivity analysis and computational uncertainty with applications to control of nonlinear parabolic partial differential equations John Allen Burns , Lisa G. Mathematical 3D modelling and sensitivity analysis of multipolar radiofrequency ablation in the spine. Janine Matschek , E.

      Solve PDE via Laplace transforms

      References Publications referenced by this paper. Lisa G.