• Journal of the Chungcheong Mathematical Society
• /
• v.27 no.3
• /
• pp.393-401
• /
• 2014

In this work, we discuss the existence of mild solutions in the ${\alpha}$-norm for some partial functional integrodifferential equations with infinite delay. We assume that the linear part generates an analytic semigroup on a Banach space X and the nonlinear part is a Lipschitz continuous function with respect to the fractional power norm of the linear part.

• Corrosion Science and Technology
• /
• v.8 no.2
• /
• pp.45-52
• /
• 2009

The corrosive behavior of mild steel in 0.05 M to 10 M $H_2SO_4$ solutions containing different concentrations of tetrahydropyrimidine derivatives (THPM) was investigated using weight loss method, gasometric technique, electrochemical studies which include AC - impedance and potentiodynamic polarization method, atomic absorption studies and synergistic effect. The results obtained reveal that THPM derivatives is an efficient mixed type inhibitor but slightly anodic and it is more effective in reducing corrosion of mild steel in $H_2SO_4$ media. The adsorption of the inhibitor on the mild steel surface obeys the Langmuir adsorption isotherm. The thermodynamic parameters of adsorption reveal a strong interaction and spontaneous adsorption of THPM on the mild steel surface. The influence of temperature and inhibitor concentration on the corrosion of mild steel has also been investigated.

• Journal of Ocean Engineering and Technology
• /
• v.18 no.2
• /
• pp.18-24
• /
• 2004

In this study, the Mild slope equation is extended to both rapidly varying topography and nonlinear waves, using the Hamiltonian principle. It is shown that this equation is equivalent to the modified mild-slope equation (Kirby and Misra, 1998) for small amplitude wave, and it is the same form with the nonlinear mild-slope equation (Isobe, 1994) for slowly varying bottom topography. Comparing its numerical solutions with the results of some hydraulic experiments, there is good agreement between them.

• Journal of Korean Society of Coastal and Ocean Engineers
• /
• v.20 no.5
• /
• pp.461-471
• /
• 2008

An analytical solution of one dimensional mild slope equation is derived by use of the WKB method, which has a form similar to Porter's solution(2003). The present solution is so general in the sense of application that it is comparable to the corresponding numerical solutions. In the derivation we also presented the solution of refraction equation in terms of surface displacement. Some numerical results of the present solution by use of Bremmer's method are presented which agree with existing numerical solutions.

• Journal of the Chungcheong Mathematical Society
• /
• v.31 no.1
• /
• pp.13-27
• /
• 2018

By using of the Banach fixed point theorem, the theory of a strongly continuous semigroup of operators and resolvent operator, we investigate the existence and uniqueness of S-asymptotically ${\omega}-periodic$ mild solutions for some differential (integrodifferential) equations with piecewise constant argument when specially ${\omega}$ is an integer.

• Journal of Applied and Pure Mathematics
• /
• v.4 no.1_2
• /
• pp.9-26
• /
• 2022

The purpose of this work is to study the existence and continuous dependence on neutral stochastic partial integrodifferential equations with impulsive effects, perturbed by a fractional Brownian motion with Hurst parameter $H{\in}({\frac{1}{2}},\;1)$. We use the theory of resolvent operators developed in Grimmer [19] to show the existence of mild solutions. Further, we establish a new impulsive-integral inequality to prove the exponential stability of mild solutions in the mean square moment. Finally, an example is presented to illustrate our obtained results.

• Journal of the Korean Mathematical Society
• /
• v.49 no.1
• /
• pp.113-138
• /
• 2012

We construct a mild solutions of the Navier-Stokes equations in half spaces for nondecaying initial velocities. We also obtain the uniform bound of the velocity field and its derivatives.

• Communications of the Korean Mathematical Society
• /
• v.21 no.3
• /
• pp.543-558
• /
• 2006

We consider a type of large deviation Principle(LDP) using Freidlin-Wentzell exponential estimates for the solutions to perturbed stochastic differential equations(SDEs) driven by Martingale measure(Gaussian noise). We are using exponential tail estimates and exit probability of a diffusion process. Referring to Freidlin-Wentzell inequality, we want to show another approach to get LDP for the solutions to SDEs.

• Journal of the Korean Mathematical Society
• /
• v.56 no.1
• /
• pp.149-167
• /
• 2019

In this work, we study the existence, uniqueness and stability in the ${\alpha}$-norm of solutions for some stochastic partial functional integrodifferential equations. We suppose that the linear part has an analytic resolvent operator in the sense given in Grimmer [8] and the nonlinear part satisfies a $H{\ddot{o}}lder$ type condition with respect to the ${\alpha}$-norm associated to the linear part. Firstly, we study the existence of the mild solutions. Secondly, we study the exponential stability in pth moment (p > 2). Our results are illustrated by an example. This work extends many previous results on stochastic partial functional differential equations.

• Journal of the Chungcheong Mathematical Society
• /
• v.28 no.3
• /
• pp.365-375
• /
• 2015

Of concern is the existence, uniqueness, and continuous dependence of a mild solution of a nonlocal Cauchy problem for a semilinear mixed Volterra-Fredholm functional integrodifferential equation. Our analysis is based on the theory of a strongly continuous semigroup of operators and the Banach fixed point theorem.