• Proceedings of the SCSK Conference
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• 2003.09b
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• pp.369-369
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• 2003

Viscarin is a tradename given to viscosifying carrageenans manufactured by FMC BioPolymer. The suitability of Vis car ins as rheology agents in mild cleansing applications has been investigated. Rheological properties, foam volume and clarity were measured to determine the impact of including 1 % Viscarin on 10% solutions of the following surfactants: acylglutamate, cocoamidopropyl betaine, PEG-80 laurate, sodium lauryl sulphate and sodium lauryol sarcosinate. Viscosity, pseudoplasticity and thixotropy of Viscarin/surfactant solutions varied with surfactant type. In all cases, the addition of Viscarin substantially increased viscosity. For example, at a shear rate of 1 sol, all surfactant solutions had viscosities <0.1 Pa s while viscosities of Viscarin/surfactant solutions ranged from 10 to 60 Pa s. By comparison, a solution of 1 % Viscarin had a viscosity of 0.3 Pa s. Clarity of surfactant solutions decreased in all cases on the addition of Viscarin. However, it was found that by including a mild solubilizing surfactant, such as PEG 40 hydrogenated castor oil, crystal clarity could be maintained in Viscarin/surfactant solutions. Viscarin increased the foam volume of sodium lauryolsarcosinate solutions from 10 ml to 220 ml and had no impact on the foam volume of the other surfactants tested. These results were used to formulate a clear, ultra-mild foaming cleansing gel based on sodium lauryol sarcosinate and Viscarin without the need for a secondary, foam-boasting surfactant. A mild shampoo was also formulated. Both products have excellent skin-feel and are capable of suspending bubbles and solid inclusions.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.15 no.4
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• pp.253-265
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• 2011

In this paper, we study the existence of mild solutions for double perturbed impulsive neutral functional evolution equations with infinite delay in Banach spaces. The existence of mild solutions to such equations is obtained by using the theory of the Hausdorff measure of noncompactness and Darbo fixed point theorem, without the compactness assumption on associated evolution system. An example is provided to illustrate the theory.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.4
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• pp.793-800
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• 2010

We investigate the existence and uniqueness of almost automorphic mild solutions of the semilinear abstract differential equations.

• Journal of the Korean Mathematical Society
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• v.57 no.1
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• pp.61-88
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• 2020

In this paper, we investigate the existence of mild solutions for a class of fractional impulsive evolution equation with periodic boundary condition by means of the method of upper and lower solutions and monotone iterative method. Using the theory of Kuratowski measure of noncompactness, a series of results about mild solutions are obtained. Finally, two examples are given to illustrate our results.

• Communications of the Korean Mathematical Society
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• v.32 no.2
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• pp.457-466
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• 2017

We study the existence and uniqueness of S-asymptotically ${\omega}-periodic$ mild solutions for some partial functional integrodifferential equations with infinite delay and nonlocal conditions.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.2
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• pp.345-352
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• 2015

We study the existence of mild solutions of partial neutral integrodifferential equations with unbounded delay by using the fixed point criterion for condensing operators.

• Bulletin of the Korean Mathematical Society
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• v.56 no.6
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• pp.1447-1465
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• 2019

In this paper, the relativistic Vlasov-Klein-Gordon system in one dimension is investigated. This non-linear dynamics system consists of a transport equation for the distribution function combined with Klein-Gordon equation. Without any assumption of continuity or compact support of any initial particle density $f_0$, we prove the existence and uniqueness of the mild solution via the iteration method.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.24 no.2
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• pp.229-242
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• 2020

Functional fractional differential inclusions with impulse effects in general Banach spaces are studied. We discuss the situation when the semigroup generated by the linear part is equicontinuous and the multifunction is Caratheodory. First, we define the PC-mild solutions for functional fractional semilinear impulsive differential inclusions. We then prove the existence of PC-mild solutions for such inclusions by using the fixed point theorem, multivalued properties and applications of NCHM (noncompactness Hausdorff measure). Eventually, we enhance the acquired results by giving an example.

• Bulletin of the Korean Mathematical Society
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• v.57 no.6
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• pp.1393-1408
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• 2020

In this paper we mainly study existence and regularity of mild solutions to the parabolic-elliptic system of drift-diffusion type with small initial data in Fourier-Besov spaces. To be more detailed, we will explain that global-in-time mild solutions are well-posed and Gevrey regular by means of multilinear singular integrals and Fourier localization argument. Furthermore, we can get time decay rate estimate of mild solutions in Fourier-Besov spaces.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.1
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• pp.89-97
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• 2014

We study the existence of mild solutions for neutral differential equations with nonlocal conditions in the ${\alpha}$-norm.