Existence and convergence results of meromorphic solutions to the equilibrium system with angular velocity

Bo Meng

doi:10.1186/s13661-019-1197-x

Abstract

We study the equilibrium system with angular velocity for the prey. This system is a generalization of the two-species equilibrium model with Neumann type boundary condition. Firstly, we consider the asymptotical stability of equilibrium points to the system of ordinary differential equations type. Then, the existence of meromorphic solutions and the stability of equilibrium points to the system of weakly coupled meromorphic type are discussed. Finally, the existence of nonnegative meromorphic solutions to the system of strongly coupled meromorphic type is investigated, and the asymptotic stability of unique positive equilibrium point of the system is proved by constructing meromorphic functions.

Highlights

The equilibrium system with angular velocity is noted for its pattern-forming behavior and has been widely used as a model for the study of obstacle problems involving reservoir simulation
It has been used to model patterns in simple fluids and in a variety of complex fluids and biological materials, such as neural tissue [3, 7]. These problems are widely studied and very well used in many areas of mathematics and physics, see [3, 5, 6, 9]. Since it was initiated by Paul Dirac in order to get a form of quantum theory compatible with special relativity, the Dirac equation has been playing a critical role in some fields of mathematics and physics, such as quantum mechanics, Clifford analysis, and partial differential equations
As one of the universal equilibrium systems used in the description of pattern formation in spatially extended dissipative systems, the general equilibrium differential equation can be found in the study of convective hydrodynamics, plasma confinement in toroidal devices, viscous film flow, and bifurcating solutions of the modified equilibrium differential equation [6, 10, 11]

Summary

Introduction

The equilibrium system with angular velocity is noted for its pattern-forming behavior and has been widely used as a model for the study of obstacle problems involving reservoir simulation. Motivated and inspired by the references [18,19,20,21], in this paper we further consider the following universal equilibrium equations with nondifferentiable boundary conditions: ; (C2) |ai( i, σi)| ≤ di i i · σi i for any i, σi ∈ Hi. Let bi : Hi × Hi → R be a map with nondifferentiable terms such that (C3) bi is a linear function for the first variable; (C4) bi is a convex function; (C5) There exists a positive constant γi satisfying γi i i · σi i ≥ ai( i, σi) for any i, σi ∈ Hi. bi( i, σi – wi) ≥ bi( i, σi) – bi( i, wi) for any i, σi, wi ∈ Hi. Based on the above notations, we define the proposed system of generalized nonlinear variational inequality problems as follows: Find (x, y) ∈ H1 × H2 such that

Results

Conclusion