• Bulletin of the Korean Mathematical Society
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• v.56 no.3
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• pp.555-561
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• 2019

In this paper we consider degenerate compressible Navier-Stokes equations giving rise to a variety of mathematical problems in many areas. We study the long time behavior for the degenerate compressible Navier-Stokes equations with damping.

• Journal of applied mathematics & informatics
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• v.38 no.5_6
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• pp.427-438
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• 2020

In this paper we define a new degenerate Bell-Carlitz polynomials. It also derives the differential equations that occur in the generating function of the degenerate Bell-Carlitz polynomials. We establish some new identities for the degenerate Bell-Carlitz polynomials. Finally, we perform a survey of the distribution of zeros of the degenerate Bell-Carlitz polynomials.

• Bulletin of the Korean Mathematical Society
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• v.53 no.6
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• pp.1597-1612
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• 2016

There are fruitful results on degenerate parabolic-hyperbolic equations recently following the idea of $Kru{\check{z}}kov^{\prime}s$ doubling variables device. This paper is devoted to the well-posedness of nonhomogeneous boundary problem for degenerate parabolic-hyperbolic equations with spatially dependent second order operator, which has not caused much attention. The novelty is that we use the boundary flux triple instead of boundary layer to treat this problem.

• Journal of the Korean Mathematical Society
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• v.37 no.6
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• pp.915-927
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• 2000

This paper is concerned with degenerate Volterra equations Mu(t) + ∫(sub)0(sup)t k(t-s) Lu(s)ds = f(t) in Banach spaces both in the hyperbolic case, and the parabolic one. The key assumption is played by the representation of the underlying space X as a direct sum X = N(T) + R(T), where T is the bounded linear operator T = ML(sup)-1. Hyperbolicity means that the part T of T in R(T) is an abstract potential operator, i.e., -T(sup)-1 generates a C(sub)0-semigroup, and parabolicity means that -T(sup)-1 generates an analytic semigroup. A maximal regularity result is obtained for parabolic equations. We will also investigate the cases where the kernel k($.$) is degenerated or singular at t=0 using the results of Pruss[8] on analytic resolvents. Finally, we consider the case where $\lambda$ is a pole for ($\lambda$L + M)(sup)-1.

• Bulletin of the Korean Mathematical Society
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• v.53 no.4
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• pp.1149-1156
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• 2016

In this paper, we introduce the degenerate Carlitz q-Bernoulli numbers and polynomials and give some interesting identities and properties of these numbers and polynomials which are derived from the generating functions and p-adic integral equations.

• Journal of the Korean Mathematical Society
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• v.58 no.5
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• pp.1279-1298
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• 2021

The aim of this paper is to prove the existence of the global attractor of the Cauchy problem for a semilinear degenerate hyperbolic equation involving strongly degenerate elliptic differential operators. The attractor is characterized as the unstable manifold of the set of stationary points, due to the existence of a Lyapunov functional.

• Bulletin of the Korean Mathematical Society
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• v.49 no.4
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• pp.669-684
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• 2012

Using the minimax methods in critical point theory, we study the multiplicity of solutions for a class of degenerate Dirichlet problem in the case near resonance.

• Journal of the Korean Institute of Telematics and Electronics
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• v.26 no.11
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• pp.1850-1856
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• 1989

For determining motion/structure of a 3-D rigid object from point correspondences over two perspective views, a linear algorithm was developed in Refs. 3 and 4. This algorithm fails when the 3-D points under observation satisfy certain geometrical constraints, as demonstrated in Refs. 7 and 8. In the present paper, we show that the linear algorithm can be resurrected in these degenerate cases by adding additional lower order polynomial constraints to original equations.

• Korean Journal of Mathematics
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• v.5 no.2
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• pp.151-167
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• 1997

We estimate the interior Lipschitz norm and maximum of the solution for degenerate parabolic equations with absorption. Also obtain the growth rate of the solution $u$ in terms of time $t$. From this we show the uniqueness of solution with respect to the initial trace.

• Communications of the Korean Mathematical Society
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• v.28 no.4
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• pp.751-766
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• 2013

We study the existence and long-time behavior of solutions to the following semilinear degenerate parabolic equation on $\mathbb{R}^N$: $$\frac{{\partial}u}{{\partial}t}-div({\sigma}(x){\nabla}u+{\lambda}u+f(u)=g(x)$$, under a new condition concerning a variable non-negative diffusivity ${\sigma}({\cdot})$. Some essential difficulty caused by the lack of compactness of Sobolev embeddings is overcome here by exploiting the tail-estimates method.