APPLICATION OF WEAK EQUIVALENCE TRANSFORMATIONS TO A GROUP ANALYSIS OF A DRIFT-DIFFUSION MODEL

@article{Romano1999APPLICATIONOW,
  title={APPLICATION OF WEAK EQUIVALENCE TRANSFORMATIONS TO A GROUP ANALYSIS OF A DRIFT-DIFFUSION MODEL},
  author={Vittorio Romano and Mariano Torrisi},
  journal={Journal of Physics A},
  year={1999},
  volume={32},
  pages={7953-7963}
}
A group analysis of a class of drift-diffusion systems is performed. In account of the presence of arbitrary constitutive functions, we look for Lie symmetries starting from the weak equivalence transformations. Applications to the transport of charges in semiconductors are presented and a special class of solutions is given for particular doping profiles. 

An Application of Equivalence Transformations to Reaction Diffusion Equations

By using an equivalence generator, derived in a previous paper, the authors apply a projection theorem to determine some special forms of the constitutive functions that allow the extension by one of the two-dimensional principal Lie algebra.

A group classification of the general second-order coupled diffusion system

We classify second-order systems of coupled heat-diffusion equations. The underlying system contains several unknown functions, the forms of which are specified via the method of group

A group analysis via weak equivalence transformations for a model of tumour encapsulation

A symmetry reduction of a PDEs system, describing the expansive growth of a benign tumour, is obtained via a group analysis approach via the use of weak equivalence transformations.

On the equivalence groups for (2+1) dimensional nonlinear diffusion equation

  • S. Özer
  • Mathematics, Physics
    Nonlinear Analysis: Real World Applications
  • 2018

Group classification of coupled partial differential equations with applications to flow in a collapsible channel and diffusion processes

The main purpose of this work is to perform the symmetry classification of the coupled systems of partial differential equations modelling flow in a collapsible tube and diffusion phenomenon. The

Symmetry analysis and exact invariant solutions for a class of energy-transport models of semiconductors

The symmetry classification of a class of energy-transport models for semiconductors is performed. Reduced systems and examples of exact invariant solutions are shown.

Equivalence Groups and Differential Invariants for (2+1) dimensional Nonlinear Diffusion Equation

(2+1) dimensional diffusion equation is considered within the framework of equivalence transformations. Generators for the group are obtained and admissible transformations between linear and

References

SHOWING 1-10 OF 21 REFERENCES

A group analysis approach for a nonlinear differential system arising in diffusion phenomena

We consider a class of second‐order partial differential equations which arises in diffusion phenomena and, following a new approach, we look for a Lie invariance classification via equivalence

Nonlocal symmetries. Heuristic approach

A constructive method for constructing nonlocal symmetries of differential equations based on the Lie—Bäcklund theory of groups is developed. The concept of quasilocal symmetries is introduced. With

Modern Group Analysis: Advanced Analytical and Computational Methods in Mathematical Physics

Some remarks on a class of ordinary differential equations: the Riccati property, differential-algebraic and differential-geometric approach to the study of involutive symbols, and the bihamiltonian approach to integrable systems.

Preliminary group classification of equations vtt=f(x,vx)vxx+g(x,vx)

The paper is one of few applications of a new algebraic approach to the problem of group classification: the method of preliminary group classification.

Applications of lie groups to differential equations

1 Introduction to Lie Groups.- 1.1. Manifolds.- Change of Coordinates.- Maps Between Manifolds.- The Maximal Rank Condition.- Submanifolds.- Regular Submanifolds.- Implicit Submanifolds.- Curves and

The drift diffusion equation and its applications in MOSFET modeling

1 Boltzmann's Equation.- 1.1 Introduction.- 1.2 Many-Body System in Equilibrium.- 1.2.1 Quantum Mechanics of Many-Body Systems.- 1.2.2 Green's Functions for Electrons.- 1.2.3 Self-Energy.- 1.2.4

Analysis and simulation of semiconductor devices

1. Introduction.- 1.1 The Goal of Modeling.- 1.2 The History of Numerical Device Modeling.- 1.3 References.- 2. Some Fundamental Properties.- 2.1 Poisson's Equation.- 2.2 Continuity Equations.- 2.3