• Bulletin of the Korean Mathematical Society
• /
• v.55 no.4
• /
• pp.1161-1178
• /
• 2018

In this paper, we consider the Cauchy problem for a class of nonlinear sixth-order wave equation. The global existence and the finite time blow-up for the problem are proved by the potential well method at both low and critical initial energy levels. Furthermore, we present some sufficient conditions on initial data such that the weak solution exists globally at supercritical initial energy level by introducing a new stable set.

• Bulletin of the Korean Mathematical Society
• /
• v.51 no.6
• /
• pp.1697-1710
• /
• 2014

The initial-boundary value problem for a class of nonlinear higher-order wave equations system with a damping and source terms in bounded domain is studied. We prove the existence of global solutions. Meanwhile, under the condition of the positive initial energy, it is showed that the solutions blow up in the finite time and the lifespan estimate of solutions is also given.

• Journal of the Korean Mathematical Society
• /
• v.44 no.4
• /
• pp.779-786
• /
• 2007

In this note, we consider a system of two reaction-diffusion equations with absorption, under homogeneous Dirichlet boundary. Using scaling methods, we establish the blow-up rate estimates.

• Honam Mathematical Journal
• /
• v.40 no.4
• /
• pp.771-783
• /
• 2018

This paper, we investigate a strongly damped nonlinear Klein-Gordon equation with nonlinearities of variable exponent type $$u_{tt}-{\Delta}u-{\Delta}u_t+m^2u+{\mid}u_t{\mid}^{p(x)-2}u_t={\mid}u{\mid}^{q(x)-2}u$$ associated with initial and Dirichlet boundary conditions in a bounded domain. We obtain a nonexistence of solutions if variable exponents p (.), q (.) and initial data satisfy some conditions.

• Journal of the Chungcheong Mathematical Society
• /
• v.23 no.4
• /
• pp.773-784
• /
• 2010

The existence of solutions in Besov spaces for nonlinear heat equations having transcendental nonlinearity: $$\frac{\partial}{{\partial}t}u-{\Delta}u=F(u)$$ is investigated. In particular, it is proved the local existence and blow-up phenomena of the solutions in Besov spaces for nonlinear heat equations corresponding to two transcendental nonlinear functions $F(u){\equiv}{\mid}u{\mid}e^{u^2}$ and $F(u){\equiv}e^u$ of rapid growth.

• Archives of Craniofacial Surgery
• /
• v.14 no.1
• /
• pp.24-29
• /
• 2013

Background: The incidence of blow out fractures is increasing and the techniques of diagnosis and treatment have been recently evolving. Despite its clinical significance, there has been no study on orbital inferiomedial blow out fractures. Therefore, this study was designed to investigate the clinical significance of treatment of orbital inferiomedial blow out fractures. Methods: A retrospective review of fifty-seven patients who could be followed up for at least 1 year after surgical reconstruction of pure inferiomedial blow out fracture was undertaken. The transconjunctival approach was performed in all cases. The onlay technique was used in 32 patients and the inlay/sheet method was used in 25 patients. We evaluated the clinical outcomes using the chi-square test. Results: In the group using the onlay technique, postoperative diplopia and enophthalmos were observed in 14 cases and 3 cases, respectively. Of these, 5 cases and 3 cases lasted for more than 6 months, respectively. In the group using the inlay/sheet method, postoperative diplopia was observed in 9 cases, but there were no cases of enophthalmos. Among the 9 diplopia cases, 4 lasted for more than 6 months. Conclusion: Postoperative diplopia and enophthalmos were increased after treatment of inferiomedial blow out fractures compared to isolated medial (0.6%, 0.3%) or inferior (1.8%, 0.6%) blow out fractures. Therefore, careful dissection is necessary not to injure the inferior oblique muscle to decrease the incidence of postoperative diplopia. Moreover, the inlay/sheet method is an effective option for reconstruction of inferiomedial blow out fractures.

• Bulletin of the Korean Mathematical Society
• /
• v.55 no.1
• /
• pp.267-296
• /
• 2018

This paper studies the Cauchy problem and blow-up phenomena for a new generalized Camassa-Holm equation with cubic nonlinearity in the nonhomogeneous Besov spaces. First, by means of the Littlewood-Paley decomposition theory, we investigate the local well-posedness of the equation in $B^s_{p,r}$ with s > $max\{{\frac{1}{p}},\;{\frac{1}{2}},\;1-{\frac{1}{p}}\},\;p,\;r{\in}[0,{\infty}]$. Second, we prove that the equation is locally well-posed in $B^s_{2,r}$ with the critical index $s={\frac{1}{2}}$ by virtue of the logarithmic interpolation inequality and the Osgood's Lemma, and it is shown that the data-to-solution mapping is $H{\ddot{o}}lder$ continuous. Finally, we derive two kinds of blow-up criteria for the strong solution by using induction and the conservative property of m along the characteristics.

• Archives of Craniofacial Surgery
• /
• v.10 no.1
• /
• pp.23-28
• /
• 2009

Purpose: Blow out fracture can present tenderness, swelling, enophthalmos, extraoccular muscle limitation, paresthesia, diplopia according to severity of injury, so reconstruction of blow out fracture is important. Orbital soft tissue should be in orbit and defected orbital wall should be corrected by autologus tissue or alloplastic implants. Every implants have their merits and faults, every implants are used various. This study was designed to compare the sequelae of blow-out fracture repair using the alloplastic implants: micro-titanium mesh(Micro Dynamic titanium $mesh^{(R)}$, Leibinger, Germany), porous polyethylene ($Medpor^{(R)}$, Porex, USA), absorbable mesh plate(Biosorb $FX^{(R)}$ . Bionx Implants Ltd, Finland). Methods: Between January 2006 and April 2008, 52 patients were included in a retrospective study analysing the outcome of corrected inferior orbital wall fracture with various kind of implants. Implants were inserted through subciliary incision. Twenty patients were operated with micro-titanium mesh, fourteen patients with porous polyethylene and eighteen patients with absorbable mesh plate. In comparative category, enophthalmos, diplopia, range of motion of extraoccular muscle, inferior orbital nerve injury were more on frequently statistically in patients. Results: Fourteen of 18 patients underwent surgical repair to improve diplopia, 11 of 17 patients to improve parasthesia, 11 of 15 patients to improve enophthalmos, 8 of 9 patients to improve extraoccular muscle limitation. Duration of follow-up time ranged from 6 months to 12 months(mean, 7.4 months). There was no statistic difference of sequelae between micro titanium mesh and porous polyethylene and absorbable mesh plate in blowout fracture, inferior wall. Conclusion: There is no difference of sequelae between micro-titanium mesh, porous polyethylene and absorbable mesh plate in blow-out fracture, inferior wall. The other factors such as defect size, location, surgeon's technique, may influence the outcome of blow-out fracture repair.

• Honam Mathematical Journal
• /
• v.19 no.1
• /
• pp.61-69
• /
• 1997

• Honam Mathematical Journal
• /
• v.19 no.1
• /
• pp.71-80
• /
• 1997