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- Peter A. Markowich

Mathematics

Saudi Arabia

2023

Discipline name
D-index
D-index (Discipline H-index) only includes papers and citation values for an examined
discipline in contrast to General H-index which accounts for publications across all
disciplines.
Citations
Publications
World Ranking
National Ranking

Mathematics
D-index
52
Citations
15,297
186
World Ranking
681
National Ranking
7

2023 - Research.com Mathematics in Saudi Arabia Leader Award

- Quantum mechanics
- Mathematical analysis
- Partial differential equation

His primary areas of investigation include Mathematical analysis, Schrödinger equation, Classical mechanics, Planck constant and Semiclassical physics. His Mathematical analysis research incorporates themes from Applied mathematics and Nonlinear system. Peter A. Markowich focuses mostly in the field of Nonlinear system, narrowing it down to topics relating to Numerical analysis and, in certain cases, Gross–Pitaevskii equation.

His work deals with themes such as Wigner distribution function, Quantum and Phase space, which intersect with Schrödinger equation. His Planck constant research integrates issues from Invariant, Classical limit and Quantum hydrodynamics. While the research belongs to areas of Semiclassical physics, Peter A. Markowich spends his time largely on the problem of Limit, intersecting his research to questions surrounding Boundary value problem, Scattering and Macroscopic quantum phenomena.

- Semiconductor equations (1405 citations)
- Homogenization limits and Wigner transforms (488 citations)
- Numerical solution of the Gross--Pitaevskii equation for Bose--Einstein condensation (397 citations)

His primary scientific interests are in Mathematical analysis, Nonlinear system, Classical mechanics, Boundary value problem and Schrödinger equation. His Partial differential equation, Poisson's equation, Singular perturbation, Numerical analysis and Asymptotic expansion investigations are all subjects of Mathematical analysis research. The Nonlinear system study combines topics in areas such as Bose–Einstein condensate, Spectral method, Statistical physics, Uniqueness and Applied mathematics.

The concepts of his Classical mechanics study are interwoven with issues in Quantum, Classical limit, Quantum hydrodynamics and Gross–Pitaevskii equation. His Boundary value problem research is multidisciplinary, incorporating elements of Eigenvalues and eigenvectors and Ordinary differential equation, Differential equation. His work carried out in the field of Schrödinger equation brings together such families of science as Mathematical physics and Semiclassical physics.

- Mathematical analysis (47.41%)
- Nonlinear system (18.10%)
- Classical mechanics (13.36%)

- Mathematical analysis (47.41%)
- Applied mathematics (11.64%)
- Limit (9.05%)

His main research concerns Mathematical analysis, Applied mathematics, Limit, Statistical physics and Partial differential equation. His studies deal with areas such as Time evolution, Square and Relaxation as well as Mathematical analysis. His work on Ode as part of general Applied mathematics research is frequently linked to Model parameters, bridging the gap between disciplines.

His Statistical physics study incorporates themes from Network formation and Boundary. Peter A. Markowich has researched Dynamical systems theory in several fields, including Balanced flow and Classical mechanics. His Schrödinger equation study frequently draws connections to adjacent fields such as Nonlinear system.

- Continuous data assimilation for the three-dimensional Brinkman-Forchheimer-extended Darcy model (51 citations)
- Notes on a PDE System for Biological Network Formation (25 citations)
- Biological transportation networks: Modeling and simulation (21 citations)

- Quantum mechanics
- Mathematical analysis
- Partial differential equation

Mathematical analysis, Partial differential equation, Applied mathematics, Network formation and Discretization are his primary areas of study. His Mathematical analysis study integrates concerns from other disciplines, such as Inverse and Square. His Partial differential equation research includes elements of Isotropy, Dynamical systems theory and Classical mechanics.

Peter A. Markowich combines subjects such as State and Graph with his study of Applied mathematics. His work in Network formation covers topics such as Statistical physics which are related to areas like Limit, Continuum and Function. In Discretization, Peter A. Markowich works on issues like Finite element method, which are connected to Reaction–diffusion system.

This overview was generated by a machine learning system which analysed the scientist’s body of work. If you have any feedback, you can contact us here.

Semiconductor equations

Peter A. Markowich;Christian A. Ringhofer;Christian Schmeiser.

**(1990)**

2441 Citations

A system of convection—diffusion equations with small diffusion coefficient arising in semiconductor physics

Peter A Markowich;Peter Szmolyan.

Journal of Differential Equations **(1989)**

2091 Citations

The Stationary Semiconductor Device Equations

Peter A. Markowich.

**(1985)**

799 Citations

Homogenization limits and Wigner transforms

Patrick Gérard;Peter A. Markowich;Norbert J. Mauser;Frédéric Poupaud.

Communications on Pure and Applied Mathematics **(1997)**

672 Citations

Numerical solution of the Gross--Pitaevskii equation for Bose--Einstein condensation

Weizhu Bao;Dieter Jaksch;Peter A. Markowich.

Journal of Computational Physics **(2003)**

640 Citations

ON CONVEX SOBOLEV INEQUALITIES AND THE RATE OF CONVERGENCE TO EQUILIBRIUM FOR FOKKER-PLANCK TYPE EQUATIONS

Anton Arnold;Peter Markowich;Giuseppe Toscani;Andreas Unterreiter.

Pediatric Dermatology **(2001)**

490 Citations

On time-splitting spectral approximations for the Schrödinger equation in the semiclassical regime

Weizhu Bao;Shi Jin;Peter A. Markowich.

Journal of Computational Physics **(2002)**

448 Citations

Entropy dissipation methods for degenerate parabolic problems and generalized Sobolev inequalities

J. A. Carrillo;A. Jüngel;P. A. Markowich;G. Toscani.

Monatshefte für Mathematik **(2001)**

402 Citations

Global Solutions to the Coupled Chemotaxis-Fluid Equations

Renjun Duan;Alexander Lorz;Peter A. Markowich.

Communications in Partial Differential Equations **(2010)**

292 Citations

Kinetic Models for Chemotaxis and their Drift-Diffusion Limits

Fabio A. C. C. Chalub;Peter A. Markowich;Benoît Perthame;Christian Schmeiser.

Monatshefte für Mathematik **(2004)**

289 Citations

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