EXISTENCE AND MAXIMAL REGULARITY OF SOLUTIONS IN L_2(R^2) FOR A HYPERBOLIC TYPE DIFFERENTIAL EQUATION WITH QUICKLY GROWING COEFFICIENTS

2020 ◽  
Vol 11 (1) ◽  
pp. 95-100
Author(s):  
Mussakan Muratbekov ◽  
◽  
Yerik Bayandiyev ◽  
Keyword(s):  
Differential Equation ◽  
Maximal Regularity ◽  
Hyperbolic Type ◽  
Regularity Of Solutions ◽  
Type Differential Equation

Additional spectral properties of the fourth-order Bessel-type differential equation

2005 ◽  
Vol 278 (12-13) ◽  
pp. 1538-1549 ◽  
Author(s):  
W. N. Everitt ◽  
H. Kalf ◽  
L. L. Littlejohn ◽  
C. Markett
Keyword(s):  
Differential Equation ◽  
Fourth Order ◽  
Spectral Properties ◽  
Type Differential Equation

scholarly journals STATIONARY STOCHASTIC VISCOSITY SOLUTIONS OF SPDEs

2011 ◽  
Vol 11 (04) ◽  
pp. 691-713 ◽  
Author(s):  
QI ZHANG
Keyword(s):  
Differential Equation ◽  
Stochastic Differential Equation ◽  
Viscosity Solution ◽  
Viscosity Solutions ◽  
Infinite Horizon ◽  
Parabolic Type ◽  
Regularity Of Solutions ◽  
Doubly Stochastic

In this paper, we construct the pathwise stationary stochastic viscosity solution of a parabolic type SPDE by backward doubly stochastic differential equation (BDSDE) on infinite horizon. For this, we study the existence, uniqueness and regularity of solutions of infinite horizon BDSDEs and their pathwise stationary property. Then by the correspondence between stochastic viscosity solutions of SPDEs and real-valued solutions of BDSDEs on infinite horizon, the stationary property is transferred from BDSDEs to SPDEs.

UNIFORM DECAY PROPERTIES OF LINEAR VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS

2008 ◽  
Vol 18 (01) ◽  
pp. 21-45 ◽  
Author(s):  
MONICA CONTI ◽  
STEFANIA GATTI ◽  
VITTORINO PATA
Keyword(s):  
Differential Equation ◽  
Hilbert Space ◽  
Differential Equations ◽  
Sufficient Conditions ◽  
Hyperbolic Type ◽  
Polynomial Decay ◽  
Convolution Kernel ◽  
Differential Inequalities ◽  
Uniform Decay ◽  
Decay Properties

We establish some new results concerning the exponential decay and the polynomial decay of the energy associated with a linear Volterra integro-differential equation of hyperbolic type in a Hilbert space, which is an abstract version of the equation [Formula: see text] describing the motion of linearly viscoelastic solids. We provide sufficient conditions for the decay to hold, without invoking differential inequalities involving the convolution kernel μ.

Tempering Kinetics of S45C Martensitic Steel

2006 ◽  
Vol 118 ◽  
pp. 375-380 ◽  
Author(s):  
Min Su Jung ◽  
Seok Jae Lee ◽  
Young Kook Lee
Keyword(s):  
Differential Equation ◽  
Kinetic Model ◽  
Kinetic Data ◽  
Martensitic Steel ◽  
Continuous Heating ◽  
Heating Rates ◽  
Strain Change ◽  
Type Differential Equation ◽  
Measured Strain ◽  
Kinetics Of

The strain change during the tempering of S45C martensitic steel was examined at different heating rates using a dilatometer. Tempering stages 1 and 3 corresponding to the precipitations of transition carbide and cementite were observed. Tempering kinetics at each stage was investigated from the relation between the measured strain and atomic volume change during tempering. From the tempering kinetic data, continuous heating tempering diagram was constructed and the tempering kinetic model was proposed as Zener-Hillert type differential equation.

scholarly journals Existence, uniqueness, and regularity of solutions to semilinear retarded differential equations

2004 ◽  
Vol 2004 (3) ◽  
pp. 213-219 ◽  
Author(s):  
D. Bahuguna
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Differential Equations ◽  
Mild Solution ◽  
Existence And Uniqueness ◽  
Regularity Of Solutions ◽  
Retarded Differential Equation ◽  
Retarded Differential Equations

In the present work, we consider a semilinear retarded differential equation in a Banach space. We first establish the existence and uniqueness of a mild solution and then prove its regularity under different additional conditions. Finally, we consider some applications of the abstract results.

Sign in / Sign up

Export Citation Format

Share Document