scholarly journals Global generalized solutions to the forager-exploiter model with logistic growth

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Qian Zhao ◽  
Bin Liu
Keyword(s):  
Global Existence ◽  
Generalized Solutions ◽  
Logistic Growth ◽  
Regularity Assumption ◽  
Initial Value

<p style='text-indent:20px;'>This paper presents the global existence of the generalized solutions for the forager-exploiter model with logistic growth under appropriate regularity assumption on the initial value. This result partially generalizes previously known ones.</p>

scholarly journals Global existence of solutions for a multi-phase flow: A drop in a gas-tube

2016 ◽  
Vol 13 (02) ◽  
pp. 381-415
Author(s):  
Debora Amadori ◽  
Paolo Baiti ◽  
Andrea Corli ◽  
Edda Dal Santo
Keyword(s):  
Global Existence ◽  
Existence Of Solutions ◽  
Inviscid Fluid ◽  
Phase Flow ◽  
Lagrangian Coordinates ◽  
Large Initial Data ◽  
Initial Value ◽  
Global Existence Of Solutions ◽  
Multi Phase Flow ◽  
Multi Phase

In this paper we study the flow of an inviscid fluid composed by three different phases. The model is a simple hyperbolic system of three conservation laws, in Lagrangian coordinates, where the phase interfaces are stationary. Our main result concerns the global existence of weak entropic solutions to the initial-value problem for large initial data.

scholarly journals WEAK ENTROPY SOLUTIONS OF NONLINEAR REACTION–HYPERBOLIC SYSTEMS for AXONAL TRANSPORT

2011 ◽  
Vol 21 (10) ◽  
pp. 2135-2154 ◽  
Author(s):  
HAO YAN ◽  
WEN-AN YONG
Keyword(s):  
Global Existence ◽  
Axonal Transport ◽  
Initial Value Problems ◽  
Hyperbolic Systems ◽  
Hyperbolic Type ◽  
Entropy Solutions ◽  
Initial Value ◽  
Biochemical Processes ◽  
Nonlinear Reaction ◽  
Entropy Satisfying

This paper is concerned with a class of nonlinear reaction–hyperbolic systems as models for axonal transport in neuroscience. We show the global existence of entropy-satisfying BV-solutions to the initial-value problems by using hyperbolic-type methods. Moreover, we rigorously justify the limit as the biochemical processes are much faster than the transport ones.

scholarly journals The Order Completion Method for Systems of Nonlinear PDEs: Solutions of Initial Value Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-12
Author(s):  
Jan Harm van der Walt
Keyword(s):  
Initial Value Problems ◽  
Lower Semicontinuous ◽  
Nonlinear Pdes ◽  
Generalized Solutions ◽  
Lower Semicontinuous Function ◽  
Semicontinuous Function ◽  
Initial Condition ◽  
Initial Value ◽  
Extended Sense ◽  
Order Completion

We present an existence result for generalized solutions of initial value problems obtained through the order completion method. The solutions we obtain satisfy the initial condition in a suitable extended sense, and each such solution may be represented in a canonical way through its generalized partial derivatives as nearly finite normal lower semicontinuous function.

scholarly journals Remarks on the critical nonlinear high-order heat equation

2019 ◽  
Vol 26 (1/2) ◽  
pp. 127-152
Author(s):  
Tarek Saanouni
Keyword(s):  
Global Existence ◽  
Heat Equation ◽  
Initial Value Problem ◽  
Existence Of Solutions ◽  
High Order ◽  
Well Posedness ◽  
Potential Well ◽  
Initial Value ◽  
Global Existence Of Solutions ◽  
Nonlinear High Order

The initial value problem for a semi-linear high-order heat equation is investigated. In the focusing case, global well-posedness and exponential decay are obtained. In the focusing sign, global and non global existence of solutions are discussed via the potential well method.

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