scholarly journals A trigonometric interpolation approach to mixed-type boundary problems associated with permeameter shape factors

2011 ◽  
Vol 47 (3) ◽  
Author(s):  
Harald Klammler ◽  
Kirk Hatfield ◽  
Bassel Nemer ◽  
Simon A. Mathias
Keyword(s):  
Mixed Type ◽  
Trigonometric Interpolation ◽  
Boundary Problems ◽  
Shape Factors ◽  
Type Boundary

Boundary Problems of Thermopiezoelectricity in Domains with Cuspidal Edges

2000 ◽  
Vol 7 (3) ◽  
pp. 441-460 ◽  
Author(s):  
T. Buchukuri ◽  
O. Chkadua
Keyword(s):  
Existence And Uniqueness ◽  
Three Dimensional ◽  
Bessel Potential ◽  
Manifolds With Boundary ◽  
Asymptotics Of Solutions ◽  
Boundary Problems ◽  
Neumann Type ◽  
Type Boundary ◽  
Homogeneous Anisotropic Medium ◽  
Bessel Potential Spaces

Abstract Dirichlet- and Neumann-type boundary value problems of statics are considered in three-dimensional domains with cuspidal edges filled with a homogeneous anisotropic medium. Using the method of the theory of a potential and the theory of pseudodifferential equations on manifolds with boundary, we prove the existence and uniqueness theorems in Besov and Bessel-potential spaces, and study the smoothness and a complete asymptotics of solutions near the cuspidal edges.

scholarly journals A mathematical study of diffusive logistic equations with mixed type boundary conditions

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Kazuaki Taira
Keyword(s):  
Mixed Type ◽  
Diffusion Rate ◽  
Critical Value ◽  
Initial Population ◽  
First Eigenvalue ◽  
Logistic Equations ◽  
Indefinite Weights ◽  
Recent Developments ◽  
Biological Interpretation ◽  
Type Boundary

<p style='text-indent:20px;'>The purpose of this paper is to provide a careful and accessible exposition of static bifurcation theory for a class of mixed type boundary value problems for diffusive logistic equations with indefinite weights, which model population dynamics in environments with spatial heterogeneity. We discuss the changes that occur in the structure of the positive solutions as a parameter varies near the first eigenvalue of the linearized problem, and prove that the most favorable situations will occur if there is a relatively large favorable region (with good resources and without crowding effects) located some distance away from the boundary of the environment. A biological interpretation of main theorem is that an initial population will grow exponentially until limited by lack of available resources if the diffusion rate is below some critical value; this idea is generally credited to the English economist T. R. Malthus. On the other hand, if the diffusion rate is above this critical value, then the model obeys the logistic equation introduced by the Belgian mathematical biologist P. F. Verhulst. The approach in this paper is distinguished by the extensive use of the ideas and techniques characteristic of the recent developments in partial differential equations.</p>

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