scholarly journals Necessary and Sufficient Conditions for the Unique Solvability of a Nonlinear Reaction-Diffusion Model

1998 ◽  
Vol 228 (2) ◽  
pp. 483-494 ◽  
Author(s):  
Jeffrey R. Anderson
Keyword(s):  
Diffusion Model ◽  
Unique Solvability ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Necessary And Sufficient Conditions ◽  
Nonlinear Reaction ◽  
Reaction Diffusion Model ◽  
Necessary And Sufficient

A NEW KIND OF FUZZY RELATIONAL EQUATIONS

2010 ◽  
Vol 18 (03) ◽  
pp. 333-342 ◽  
Author(s):  
FENG QIN ◽  
PING FANG
Keyword(s):  
Unique Solvability ◽  
Complete Solution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Solution Set ◽  
Fuzzy Relational Equations ◽  
Necessary And Sufficient

In this paper, a new kind of fuzzy relational equations (FREs for short) A ∘R*x = b is first introduced, and then the problem of solving solution to the FREs is discussed, where A is an m × n matrix, x and b are an n and an m dimensional column vectors, respectively. More specifically, their solvability and unique solvability are investigated, the corresponding necessary and sufficient conditions are presented, the complete solution set is obtained. It is worth noting the method to construct the complete solution set.

On the solvability of the antiperiodic boundary value problem for systems of linear generalized differential equations

2017 ◽  
Vol 24 (2) ◽  
pp. 169-184
Author(s):  
Malkhaz Ashordia
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Spectral Type ◽  
Unique Solvability ◽  
Boundary Value ◽  
Type Theorem ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Generalized Differential ◽  
Necessary And Sufficient

AbstractAn antiperiodic boundary value problem is considered for systems of linear generalized differential equations. A Green-type theorem on the unique solvability of the problem and representation of its solution are established. Effective necessary and sufficient conditions (of spectral type) are given for the unique solvability of the problem as well.

Traveling wavefronts of a nonlinear reaction–diffusion model of tumor growth under the acid environment

2014 ◽  
Vol 07 (03) ◽  
pp. 1450034
Author(s):  
Huiyan Zhu ◽  
Yang Luo ◽  
Xiufang Wang
Keyword(s):  
Diffusion Model ◽  
Perturbation Methods ◽  
Tumor Tissue ◽  
Reaction Diffusion ◽  
Traveling Wave Solution ◽  
Ion Concentration ◽  
Banach Fixed Point Theorem ◽  
Nonlinear Reaction ◽  
Reaction Diffusion Model ◽  
Acid Environment

In this paper, a reaction–diffusion model describing temporal development of tumor tissue, normal tissue and excess H+ ion concentration is considered. Based on a combination of perturbation methods, the Fredholm theory and Banach fixed point theorem, we theoretically justify the existence of the traveling wave solution for this model.

scholarly journals A solvable nonlinear reaction-diffusion model

1995 ◽  
Vol 198 (2) ◽  
pp. 100-104 ◽  
Author(s):  
Max-Olivier Hongler ◽  
Ricardo Lima
Keyword(s):  
Diffusion Model ◽  
Reaction Diffusion ◽  
Nonlinear Reaction ◽  
Reaction Diffusion Model
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