THE ASYMPTOTIC BEHAVIOUR OF SOLUTIONS OF THE SECOND BOUNDARY-VALUE PROBLEM IN UNBOUNDED DOMAINS

1980 ◽  
Vol 35 (4) ◽  
pp. 175-176
Author(s):  
S S Lakhturov
Keyword(s):  
Boundary Value Problem ◽  
Asymptotic Behaviour ◽  
Boundary Value ◽  
Unbounded Domains ◽  
Asymptotic Behaviour Of Solutions

On the asymptotic behaviour at infinity of solutions of the traction boundary value problem

1989 ◽  
Vol 111 (1-2) ◽  
pp. 33-52 ◽  
Author(s):  
B.B. Orazov
Keyword(s):  
Boundary Value Problem ◽  
Asymptotic Behaviour ◽  
Nonlinear Elasticity ◽  
Boundary Value ◽  
Asymptotic Behaviour Of Solutions

SynopsisKorn's inequalities are proved for star-shaped domains and it is shown how the constants in these inequalities depend on the dimensions of the domain. These inequalities are then used to prove a generalisation of Saint-Venant's Principle for nonlinear elasticity and additionally to establish the asymptotic behaviour of solutions to the traction boundary value problem for a non-prismatic cylinder.

An elliptic boundary value problem for strongly non-linear equations in unbounded domains

1977 ◽  
Vol 77 (3-4) ◽  
pp. 217-230 ◽  
Author(s):  
Vesa Mustonen
Keyword(s):  
Boundary Value Problem ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Linear Equations ◽  
Unbounded Domains ◽  
Elliptic Boundary Value Problem ◽  
Elliptic Boundary Value ◽  
Non Linear ◽  
Linear Elliptic Boundary ◽  
Non Linear Equations

SynopsisThe existence of a variational solution is shown for the strongly non-linear elliptic boundary value problem in unbounded domains. The proof is a generalisation to Orlicz-Sobolev space setting of the idea introduced in [15] for the equations involving polynomial non-linearities only.

scholarly journals Asymptotic behaviour of solutions for porous medium equation with periodic absorption

2001 ◽  
Vol 26 (1) ◽  
pp. 35-44 ◽  
Author(s):  
Yin Jingxue ◽  
Wang Yifu
Keyword(s):  
Porous Medium ◽  
Periodic Solution ◽  
Boundary Value Problem ◽  
Asymptotic Behaviour ◽  
Small Neighborhood ◽  
Porous Medium Equation ◽  
Direct Consequence ◽  
Medium Equation ◽  
Asymptotic Behaviour Of Solutions ◽  
Nontrivial Periodic Solutions

This paper is concerned with porous medium equation with periodic absorption. We are interested in the discussion of asymptotic behaviour of solutions of the first boundary value problem for the equation. In contrast to the equation without sources, we show that the solutions may not decay but may be “attracted” into any small neighborhood of the set of all nontrivial periodic solutions, as time tends to infinity. As a direct consequence, the null periodic solution is “unstable.” We have presented an accurate condition on the sources for solutions to have such a property. Whereas in other cases of the sources, the solutions might decay with power speed, which implies that the null periodic solution is “stable.”

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