One-dimensional aggregation equation after blow up: Existence, uniqueness and numerical simulation | Zendy

François James | Zendy; Nicolas Vauchelet | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Open Access

One-dimensional aggregation equation after blow up: Existence, uniqueness and numerical simulation

Author(s) -

François James,

Nicolas Vauchelet

Publication year - 2016

Publication title -

networks and heterogeneous media

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.732

H-Index - 34

eISSN - 1556-181X

pISSN - 1556-1801

DOI - 10.3934/nhm.2016.11.163

Subject(s) - uniqueness , mathematics , measure (data warehouse) , mathematical analysis , duality (order theory) , convergence (economics) , dimension (graph theory) , finite volume method , space (punctuation) , nonlinear system , weak solution , physics , computer science , pure mathematics , mechanics , quantum mechanics , database , economics , economic growth , operating system

The nonlocal nonlinear aggregation equation in one space dimension is investigated.In so-called attractive case smooth solutions blow up in finite time, so that weak measure solutions are introduced.The velocity involved in equation becomes discontinuous, and a particular care has to be paid to its definitionas well as formulation of corresponding flux. When this is done, notion of duality solutions allows toobtain global in time existence and uniqueness for measure solutions. An upwind finite volume scheme is also analyzed,and convergence towards unique solution is proved. Numerical examples show the dynamics of solutions after blow up time.

The content you want is available to Zendy users.

Already have an account? Click here to sign in.

Having issues? You can contact us here

Accelerating Research