9. MODERN APPROACH TO SYMMETRIES.
MATHEMATICAL MODELS IN BIOMATHEMATICS

The objectives of this course is to focus the attention of students on symmetry methods to search for exact solutions of nonlinear models in Physics, in Engineering Science, and in Biology as well as to show recent developments of the theoretical tools of the Lie group methods applicable to the study of differential equations.

Additionally, we present a brief introduction to the Mathematical Biology. This is one of the most exciting modern applications of the Mathematics. We focus in the mathematical modelling of tumour growth and the mathematical tools to understand this process.

PROGRAMME

 

Monday  June 12 nd

9.00 - 10.00  Presentation
(Dr. Stephen Anco, Brock University; Dra. Mª Luz Gandarias and Dra. Mª Santos Bruzón, University of Cádiz).

10.00 - 11.00  Modern approach to symmetries:
theory and computation. 
(Dr. Stephen Anco, Brock University).

11.00 – 11.3o  Break.

11.30 – 13.30 Integration of ordinary differential equations
using symmetries
(Dra. Mª Luz Gandarias, University of Cádiz).

 

Tuesday June 13 th

9.00 - 11.00  Invariant solutions of partial differential equations (Dra. Mª Santos Bruzón, University of Cádiz).

11.00 – 11.3o  Break.

11.30 – 12.30 General elements about models in interacting population dynamics: Balance equations, constitutive equations. (Dr. Mariano Torrisi, University of Catania).

12.30 – 13.30 General elements of invertible point transformations, symmetries and equivalence transformations (Dra. Rita Traciná, University of Catania).

 

Wednesday June 14 th

9.00 - 11.00  Symmetry reduction and solutions. Examples
(Dr. Masood Khalique, South Africa North-West University).

11.00 – 11.3o  Break.

11.30 – 12.30 Modern formulation of Noether's theorem:
theory and computation
(Dr. Stephen Anco, Brock University).

12.30 – 13.30 Generalization of Noether's theorem
to non-variational equations: theory and computation
of conservation laws
(Dr. Stephen Anco, Brock University).

 

Thursday June 15 th

9.00 - 10.00  Symmetries, adjoint-symmetries,
conservation laws, and Ibragimov's theorem
(Dr. Stephen Anco, Brock University).

10.00 - 11.00  Reaction diffusion models and their symmetries. Two cases (Dr. Mariano Torrisi, University of Catania).

11.00 – 11.3o  Break.

11.30 – 12.30 General elements of differential invariant
of equivalence transformation
(Dra. Rita Traciná, University of Catania).

12.30 – 13.30 Applications of differential invariants
to diffusion equations.
(Dr. Mariano Torrisi, University of Catania).

 

Friday June 16 th

9.00 - 10.00  Classical symmetries for a type of Fisher equation. Reductions and some exact solutions for a type of Fisher equation (Dra. Mª Rosa Durán, University of Cádiz).

10.00 - 11.00  Conservation laws for a generalized Fisher equation (Dra. Mª Rosa Durán, University of Cádiz). 
(Dr. Stephen Anco, Brock University).

11.00 – 11.3o  Break.

11.30 – 12.30 Mathematical Models in Biomedicine
with applications in tumor growth I
(Dr. Juan Belmonte, University of Castilla-La Mancha).

12.30 – 13.30 Mathematical Models in Biomedicine with applications in tumor growth II
(Dr. Juan Belmonte, University of Castilla-La Mancha).

 

Dates: June 12 nd-16 th

Course Director:
Dra. Mª Santos Bruzón Gallego

Departament of Mathematics, Faculty
of Sciences, University of Cádiz, Spain

Speakers:
Dra. Mª Santos Bruzón

Department of Mathematics, University of Cádiz

 

Dr. Stephen Anco

Department of Mathematics, Brock University, Canada

 

Dr. Mariano Torrisi

Department of Mathematics and Informatic,
University of Catania, Italy

 

Dr. Masood Khalique

Department of Mathematical Sciences,
North-West University, South Africa

 

Dra. Rita Traciná

Department of Mathematics and Informatic,
University of Catania, Italy

 

Dr. Juan Belmonte

Department of Mathematics, University of Castilla-La Mancha

 

Dra. María Rosa Durán

Department of Mathematics, University of Cádiz

 

Dra. Mª Luz Gandarias

Department of Mathematics, University of Cádiz