scholarly journals Non-radial solutions to a bi-harmonic equation with negative exponent

2019 ◽  
Vol 58 (6) ◽  
Author(s):  
Ali Hyder ◽  
Juncheng Wei
Keyword(s):  
Radial Solutions ◽  
Harmonic 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 On radial stationary solutions to a model of non-equilibrium growth

2013 ◽  
Vol 24 (3) ◽  
pp. 437-453 ◽  
Author(s):  
CARLOS ESCUDERO ◽  
ROBERT HAKL ◽  
IRENEO PERAL ◽  
PEDRO J. TORRES
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Stationary Solutions ◽  
Parabolic Partial Differential Equation ◽  
Radial Solutions ◽  
Variational Techniques ◽  
Existence And Multiplicity ◽  
Equilibrium Growth ◽  
Non Equilibrium

We present the formal geometric derivation of a non-equilibrium growth model that takes the form of a parabolic partial differential equation. Subsequently, we study its stationary radial solutions by means of variational techniques. Our results depend on the size of a parameter that plays the role of the strength of forcing. For small forcing we prove the existence and multiplicity of solutions to the elliptic problem. We discuss our results in the context of non-equilibrium statistical mechanics.

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