Asymptotic behavior of the solution of a diffusion equation with nonlocal boundary conditions | Zendy

Bhargav Kumar Kakumani | Zendy; Suman Kumar Tumuluri | Zendy

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Asymptotic behavior of the solution of a diffusion equation with nonlocal boundary conditions

Author(s) -

Bhargav Kumar Kakumani,

Suman Kumar Tumuluri

Publication year - 2016

Publication title -

discrete and continuous dynamical systems - b

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.864

H-Index - 53

eISSN - 1553-524X

pISSN - 1531-3492

DOI - 10.3934/dcdsb.2017019

Subject(s) - pointwise , mathematics , diffusion equation , infinity , mathematical analysis , nonlinear system , boundary value problem , diffusion , term (time) , physics , thermodynamics , economy , quantum mechanics , economics , service (business)

In this paper, we consider a particular type of nonlinear McKend-rick-von Foerster equation with a diffusion term and Robin boundary condition. We prove the existence of a global solution to this equation. The steady state solutions to the equations that we consider have a very important role to play in the study of long time behavior of the solution. Therefore we address the issues pertaining to the existence of solution to the corresponding state equation. Furthermore, we establish that the solution of McKendrick-von Foerster equation with diffusion converges pointwise to the solution of its steady state equations as time tends to infinity.

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