BVPSYMMETRY · Reductions and exact solutions of boundary value problems with moving boundaries by means of symmetry based methods
7РП — „Хора“ (Действия „Мария Кюри“)
- Период
- 2016-05-10 → 2017-05-09
- Финансиране от ЕС
- 15 000 €
- Участници
- 1
- Схема
- MC-IIFR
Линиите свързват координатора с партньорите.
Накратко на български
Математически методи за решаване на сложни уравнения се прилагат върху процеси като растежа на тумори или топенето на материали. Те помагат за по-точното описание на физически и биологични явления чрез сравнение между теоретични изчисления и числени данни.
Кратко обяснение, генерирано от езиков модел по текста на CORDIS. Оригиналът е по-долу.
Резултати накратко
Reductions and exact solutions of boundary value problems with moving boundaries by means of symmetry based methods
This project is a natural continuation (Return Phase) of the project 328563 with the same title, which was conducted at the University of Nottingham in 2013—2015. The development of new theoretical foundations and algorithms for the reduction of nonlinear boundary value problems (especially those with moving boundaries) to problems of lower dimensionality and the construction of exact solutions of the problems in question are the main aims of the project. An applied goal is to compare the analytical results derived with those obtained by means of the appropriate numerical techniques for some physically and biologically motivated problems. The most important results obtained can be summarised as follows: Lie symmetries, reductions and exact solutions of a (1+2)-dimensional nonlinear model of the Keller-Segel type were constructed. As a result, the relevant Neumann and Cauchy problems were exactly solved under appropriate restrictions on boundary conditions and initial profiles. Lie and Q-conditional symmetries of a well-known boundary-value problem with a free boundary describing the tumour growth processes were studied. Using the symmetry reductions, some exact solutions of the problem in question were derived and their biological interpretation established. The results were generalized on the multidimensional case under assumption that the tumour possesses a spherical symmetry. A generalization of the algorithm for the symmetry reduction, which was worked out earlier, on the boundary-value problems with more complicated boundary conditions (including a set of moving boundaries) was derived. To demonstrate the efficiency of the algorithm, a specific boundary-value problem (including multidimensional case) describing melting and evaporation of materials was studied. The results obtained have been published in two papers and a preprint, and presented at seven talks at international conferences, seminars, and workshops (see details in Section 2). The project site on Facebook with the address https://www.facebook.com/BVPsymmetry/info?tab=overview contains an appropriate information about this project for the attention of researchers, students and the general public.
Текст от CORDIS, на английски · Данни: CORDIS, © Европейски съюз
Цел на проекта
Boundary value problems with moving boundaries are widely used in mathematical modeling a huge number of processes, which arise in physics, biology and industry. While these processes can be very different from a formal point of view, they have the common peculiarity: unknown moving boundaries. The most important subclass of such boundary value problems (BVPs) is the Stefan problems, in which the movement of unknown boundaries is governed by the well-known Stefan boundary conditions. BVPs with moving boundaries, particularly the multidimensional Stefan problems, are the main object of the proposed project.Developing new theoretical foundations and algorithms for reduction of such BVPs to those of lower dimensionality and construction of exact solutions of BVPs in question is the main aim of the project. Applied goal is to compare the analytical results derived with those obtained by means of the appropriate numerical techniques in the case of a wide range of the physically and biologically motivated problems. Moreover such comparison will demonstrate the real interdisciplinary aspect of the proposal. The novel idea of the project is to develop the algorithms mentioned above using such symmetry based methods as the classical Lie-Ovsiannikov method, the Bluman-Cole method of non-classical symmetry, conditional symmetry method and their recent extensions.The main results to be achieved: new definitions of (generalized) conditional invariance for BVPs with a wide range of boundary conditions will be derived; algorithms for how to construct all possible conditional symmetries for the given class of BVPs will be determined; new analytical results (conditional symmetries, reductions and exact solutions of BVPs) will be established by application of the algorithm to a wide range of nonlinear BVPs modeling the tumour growth processes and melting-evaporation processes.
Оригинален текст от CORDIS (на английски).
Участници
- INSTITUTE OF MATHEMATICS OF THE NATIONAL ACADEMY OF SCIENCES OF UKRAINE · KyivКоординаторУкрайна
Връзки
Данни: CORDIS, © Европейски съюз