• 제어로봇시스템학회:학술대회논문집
• /
• 1993.10b
• /
• pp.355-359
• /
• 1993

This paper deals with the problem of robust TDF(Two Degree of Freedom) H$_{\infty}$ control design for a linear system with parameter uncertainty in the state space model. The uncertain system considered here is with the time-invariant norm-bounded parameter uncertainty in the state matrix. A TDF H$_{\infty}$ control design is presented which robustly stabilizes the plant, guarantees the robust H$_{\infty}$ performance and improves the tracking performance for the closed-loop system in the face of parameter uncertainty. It is shwon that a suitable stabilizing control law can be constructed in terms of a positive definite solution to a certain parameter-dependent algebraic Riccati equation and a good tracking performance can be constructed in terms of suitable feedforward control law.aw.

• Journal of the Korean Mathematical Society
• /
• v.56 no.4
• /
• pp.857-867
• /
• 2019

Suppose that G = (V, E) is a connected locally finite graph with the vertex set V and the edge set E. Let ${\Omega}{\subset}V$ be a bounded domain. Consider the following quasilinear elliptic equation on graph G $$\{-{\Delta}_{pu}={\lambda}K(x){\mid}u{\mid}^{p-2}u+f(x,u),\;x{\in}{\Omega}^{\circ},\\u=0,\;x{\in}{\partial}{\Omega},$$ where ${\Omega}^{\circ}$ and ${\partial}{\Omega}$ denote the interior and the boundary of ${\Omega}$, respectively, ${\Delta}_p$ is the discrete p-Laplacian, K(x) is a given function which may change sign, ${\lambda}$ is the eigenvalue parameter and f(x, u) has exponential growth. We prove the existence and monotonicity of the principal eigenvalue of the corresponding eigenvalue problem. Furthermore, we also obtain the existence of a positive solution by using variational methods.

• Communications of the Korean Mathematical Society
• /
• v.36 no.2
• /
• pp.247-256
• /
• 2021

Using variational methods, we show the existence of a unique weak solution of the following singular biharmonic problems of Kirchhoff type involving critical Sobolev exponent: $$(\mathcal{P}_{\lambda})\;\{\begin{array}{lll}{\Delta}^2u-(a{\int}_{\Omega}{\mid}{\nabla}u{\mid}^2dx+b){\Delta}u+cu=f(x){\mid}u{\mid}^{-{\gamma}}-{\lambda}{\mid}u{\mid}^{p-2}u&&\text{ in }{\Omega},\\{\Delta}u=u=0&&\text{ on }{\partial}{\Omega},\end{array}$$ where Ω is a smooth bounded domain of ℝⁿ (n ≥ 5), ∆² is the biharmonic operator, and ∇u denotes the spatial gradient of u and 0 < γ < 1, λ > 0, 0 < p ≤ 2^# and a, b, c are three positive constants with a + b > 0 and f belongs to a given Lebesgue space.

• Communications of the Korean Mathematical Society
• /
• v.38 no.3
• /
• pp.741-754
• /
• 2023

In this paper, we study the existence and nonexistence of solutions for a class of Hamiltonian strongly degenerate elliptic system with subcritical growth $$\left{\array{-{\Delta}_{\lambda}u-{\mu}v={\mid}v{\mid}^{p-1}v&&\text{in }{\Omega},\\-{\Delta}_{\lambda}v-{\mu}u={\mid}u{\mid}^{q-1}u&&\text{in }{\Omega},\\u=v=0&&\text{ on }{\partial}{\Omega},}$$ where p, q > 1 and Ω is a smooth bounded domain in ℝ^N, N ≥ 3. Here Δ_λ is the strongly degenerate elliptic operator. The existence of at least a nontrivial solution is obtained by variational methods while the nonexistence of positive solutions are proven by a contradiction argument.

• Journal of applied mathematics & informatics
• /
• v.29 no.3_4
• /
• pp.921-936
• /
• 2011

In this paper, our main purpose is to establish the existence of weak solutions of a weak solutions of a class of p-q-Laplacian system involving concave-convex nonlinearities: $$\{\array{-{\Delta}_pu-{\Delta}_qu={\lambda}V(x)|u|^{r-2}u+\frac{2{\alpha}}{\alpha+\beta}|u|^{\alpha-2}u|v|^{\beta},\;x{\in}{\Omega}\\-{\Delta}p^v-{\Delta}q^v={\theta}V(x)|v|^{r-2}v+\frac{2\beta}{\alpha+\beta}|u|^{\alpha}|v|^{\beta-2}v,\;x{\in}{\Omega}\\u=v=0,\;x{\in}{\partial}{\Omega}}$$ where ${\Omega}$ is a bounded domain in $R^N$, ${\lambda}$, ${\theta}$ > 0, and 1 < ${\alpha}$, ${\beta}$, ${\alpha}+{\beta}=p^*=\frac{N_p}{N_{-p}}$ is the critical Sobolev exponent, ${\Delta}_su=div(|{\nabla}u|^{s-2}{\nabla}u)$ is the s-Laplacian of u. when 1 < r < q < p < N, we prove that there exist infinitely many weak solutions. We also obtain some results for the case 1 < q < p < r < $p^*$. The existence results of solutions are obtained by variational methods.

• Journal of the Korean Crystal Growth and Crystal Technology
• /
• v.3 no.1
• /
• pp.12-17
• /
• 1993

Growth runs of KTP single crystals were carried out by the hydrothermal method. KTP powders used for the crystal growth were prepared as a single phase by the solid state reaction of a stoichiometric mixture of $KH_2PO_4 and TiO_2$ at TEX>$800^{\circ}C$ and subsequently by the hydrothermal treatment at $250^{\circ}C$ 4m KF solution. The most effective solvents for the crystal growth of KTP were KF and K $K_2HPO_4$ solutions. Solubilities of KTP in these solutions were positive over the range $350~450^{\circ}C$.Seed crystals of good quality could be obtained by the horizontal temperature gradient method at temperatures over the range 380~430^{\circ}C$ in these solutions. The hydrothermal conditions for the high growth rates of seed crystals are as follows: growth method; vertical temperature gradient method, solvent; 4m KF or $K_2HPO_4$ solution, temperature region; $400~450^{\circ}C$, pressure region; $1000~1500kg/cm^2$, where solubility of KTP was large enough to proceed the growth. Under such conditions, seed crystals of KTP are grown at a rate of approximately 0.06-0.08mm/day in the direction of the c-axis. Morphologies of grown crystals tended to be bounded by (100), (011) and (201) faces.

• Journal of the Korean Mathematical Society
• /
• v.57 no.3
• /
• pp.747-775
• /
• 2020

In this work we investigate the nonlocal elliptic equation with critical Hardy-Sobolev exponents as follows, $$(P)\;\{(-{\Delta}_p)^su={\lambda}{\mid}u{\mid}^{q-2}u+{\frac{{\mid}u{\mid}^{p{^*_s}(t)-2}u}{{\mid}x{\mid}^t}}{\hspace{10}}in\;{\Omega},\\u=0{\hspace{217}}in\;{\mathbb{R}}^N{\backslash}{\Omega},$$ where Ω ⊂ ℝ^N is an open bounded domain with Lipschitz boundary, 0 < s < 1, λ > 0 is a parameter, 0 < t < sp < N, 1 < q < p < p^∗_s where $p^*_s={\frac{N_p}{N-sp}}$, $p^*_s(t)={\frac{p(N-t)}{N-sp}}$, are the fractional critical Sobolev and Hardy-Sobolev exponents respectively. The fractional p-laplacian (-∆_p)^su with s ∈ (0, 1) is the nonlinear nonlocal operator defined on smooth functions by $\displaystyle(-{\Delta}_p)^su(x)=2{\lim_{{\epsilon}{\searrow}0}}\int{_{{\mathbb{R}}^N{\backslash}{B_{\epsilon}}}}\;\frac{{\mid}u(x)-u(y){\mid}^{p-2}(u(x)-u(y))}{{\mid}x-y{\mid}^{N+ps}}dy$, x ∈ ℝ^N. The main goal of this work is to show how the usual variational methods and some analysis techniques can be extended to deal with nonlocal problems involving Sobolev and Hardy nonlinearities. We also prove that for some α ∈ (0, 1), the weak solution to the problem (P) is in C^1,α(${\bar{\Omega}}$).

• KSBB Journal
• /
• v.9 no.3
• /
• pp.325-331
• /
• 1994

PGA is formed in a route of CO2 fixation of RuBP catalyzed by RuBPCase, followed by reduction of the PGA by NADH to GAP This reduction is enhanced in an anionic micellar solution(SDS), in which NADH is distributed in the aqueous and the micellar pseudophases in a given ratio. This micellar bounded NADH reacts to PGA, and in higher micellar concentration than $1.25{\times}10^{-2}M$, most of NADH is oxidized to NAD+ by PGA. On the other hand, in the solutions of the positive ionic(CTABr), zwitter ionic(Chaps) and nonionic (Brij and Triton X-100) micelles, the reactions are also enhanced and the concentrations of NADH reach minima with micellar concentrations. Such minima are typical of micellar catalyzed bimolecular reactions, and the fall in concentrations of the reductant followed by a gradual increase is charataristic of reactions of hydrophobic substrates: that is, the reductions of PGA by NADH are sharply enhanced in a range of the lower micellar concentrations, and NADH amounts in ca. $1.25-2.50{\times}10^{-3}M$ micellar solutions are reached to minima, followed by gradual increases of the reductant concentration.