GLOBAL ANALYSIS OF THE SHADOW GIERER-MEINHARDT SYSTEM WITH GENERAL LINEAR BOUNDARY CONDITIONS IN A RANDOM ENVIRONMENT

Kwadwo Antwi-Fordjour; Seonguk Kim; Marius Nkashama

doi:10.11948/20190306

2020 Volume 10 Issue 5

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Kwadwo Antwi-Fordjour, Seonguk Kim, Marius Nkashama. GLOBAL ANALYSIS OF THE SHADOW GIERER-MEINHARDT SYSTEM WITH GENERAL LINEAR BOUNDARY CONDITIONS IN A RANDOM ENVIRONMENT[J]. Journal of Applied Analysis & Computation, 2020, 10(5): 1980-1994. doi: 10.11948/20190306

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Kwadwo Antwi-Fordjour, Seonguk Kim, Marius Nkashama. GLOBAL ANALYSIS OF THE SHADOW GIERER-MEINHARDT SYSTEM WITH GENERAL LINEAR BOUNDARY CONDITIONS IN A RANDOM ENVIRONMENT[J]. Journal of Applied Analysis & Computation, 2020, 10(5): 1980-1994. doi: 10.11948/20190306

GLOBAL ANALYSIS OF THE SHADOW GIERER-MEINHARDT SYSTEM WITH GENERAL LINEAR BOUNDARY CONDITIONS IN A RANDOM ENVIRONMENT

1.
Department of Mathematics and Computer Science, Samford University, Birmingham, Alabama 35229, USA
2.
Department of Mathematics, DePauw University, Greencastle, Indiana 46135, USA
3.
Department of Mathematics, University of Alabama at Birmingham, Birmingham, Alabama 35294, USA

Corresponding author: Email: seongukkim@depauw.edu (S. Kim)

Abstract

Abstract

The global analysis of the shadow Gierer-Meinhardt system with multiplicative white noise and general linear boundary conditions is investigated in this paper. For this reaction-diffusion system, we employ a fixed point argument to prove local existence and uniqueness. Our results on global existence are based on a priori estimates of solutions.
- Shadow Gierer-Meinhardt system /
- multiplicative noise /
- global existence /
- linear Robin-Neumann boundary conditions
MSC: 60H05, 60H15, 60H30

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References

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