scholarly journals Infinitely many non-radial solutions to a critical equation on annulus

2018 ◽  
Vol 265 (9) ◽  
pp. 4076-4100 ◽  
Author(s):  
Yuxia Guo ◽  
Benniao Li ◽  
Angela Pistoia ◽  
Shusen Yan
Keyword(s):  
Radial Solutions ◽  
Critical Equation

scholarly journals The exterior Dirichlet problems of Monge–Ampère equations in dimension two

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Limei Dai
Keyword(s):  
Asymptotic Behavior ◽  
Unit Ball ◽  
Bounded Domain ◽  
Viscosity Solutions ◽  
Sufficient Conditions ◽  
Radial Solutions ◽  
Dirichlet Problems ◽  
Necessary And Sufficient ◽  
Monge Ampere ◽  
Prescribed Asymptotic Behavior

AbstractIn this paper, we study the Monge–Ampère equations $\det D^{2}u=f$ det D 2 u = f in dimension two with f being a perturbation of $f_{0}$ f 0 at infinity. First, we obtain the necessary and sufficient conditions for the existence of radial solutions with prescribed asymptotic behavior at infinity to Monge–Ampère equations outside a unit ball. Then, using the Perron method, we get the existence of viscosity solutions with prescribed asymptotic behavior at infinity to Monge–Ampère equations outside a bounded domain.

scholarly journals On the decay of the energy for radial solutions in Moore–Gibson–Thompson thermoelasticity

2021 ◽  
pp. 108128652199425
Author(s):  
Noelia Bazarra ◽  
José R Fernández ◽  
Ramón Quintanilla
Keyword(s):  
Numerical Simulations ◽  
Exponential Decay ◽  
Time Variable ◽  
Radial Solutions ◽  
Radially Symmetric Solutions ◽  
Thermoelastic Theory

In this paper, we consider the Moore–Gibson–Thompson thermoelastic theory. We restrict our attention to radially symmetric solutions and we prove the exponential decay with respect to the time variable. We demonstrate this fact with the help of energy arguments. Later, we give some numerical simulations to illustrate this behaviour.

A field theory approach to stability of radial equilibria in nonlinear elasticity

1986 ◽  
Vol 99 (3) ◽  
pp. 589-604 ◽  
Author(s):  
J. Sivaloganathan
Keyword(s):  
Field Theory ◽  
Calculus Of Variations ◽  
Nonlinear Elasticity ◽  
Isotropic Material ◽  
Theory Approach ◽  
Radial Solutions ◽  
Equilibrium Equations ◽  
The Stability ◽  
State Of Tension

In this paper we study the stability of a class of singular radial solutions to the equilibrium equations of nonlinear elasticity, in which a hole forms at the centre of a ball of isotropic material held in a state of tension under prescribed boundary displacements. The existence of such cavitating solutions has been shown by Ball[1], Stuart [11] and Sivaloganathan[10]. Our methods involve elements of the field theory of the calculus of variations and provide a new unified interpretation of the phenomenon of cavitation.

scholarly journals Critical equation of state of randomly dilute Ising systems

2003 ◽  
Vol 68 (13) ◽  
Author(s):  
Pasquale Calabrese ◽  
Martino De Prato ◽  
Andrea Pelissetto ◽  
Ettore Vicari
Keyword(s):  
Equation Of State ◽  
Critical Equation ◽  
Ising Systems
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