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LONG-TIME BEHAVIOR OF SOLUTIONS TO A NONLOCAL QUASILINEAR PARABOLIC EQUATION
Thuy, Le Thi,Tinh, Le Tran Korean Mathematical Society 2019 대한수학회논문집 Vol.34 No.4
In this paper we consider a class of nonlinear nonlocal parabolic equations involving p-Laplacian operator where the nonlocal quantity is present in the diffusion coefficient which depends on $L^p$-norm of the gradient and the nonlinear term is of polynomial type. We first prove the existence and uniqueness of weak solutions by combining the compactness method and the monotonicity method. Then we study the existence of global attractors in various spaces for the continuous semigroup generated by the problem. Finally, we investigate the existence and exponential stability of weak stationary solutions to the problem.
GLOBAL ATTRACTORS FOR NONLOCAL PARABOLIC EQUATIONS WITH A NEW CLASS OF NONLINEARITIES
Anh, Cung The,Tinh, Le Tran,Toi, Vu Manh Korean Mathematical Society 2018 대한수학회지 Vol.55 No.3
In this paper we consider a class of nonlocal parabolic equations in bounded domains with Dirichlet boundary conditions and a new class of nonlinearities. We first prove the existence and uniqueness of weak solutions by using the compactness method. Then we study the existence and fractal dimension estimates of the global attractor for the continuous semigroup generated by the problem. We also prove the existence of stationary solutions and give a sufficient condition for the uniqueness and global exponential stability of the stationary solution. The main novelty of the obtained results is that no restriction is imposed on the upper growth of the nonlinearities.
Global attractors for nonlocal parabolic equations with a new class of nonlinearities
Cung The Anh,Le Tran Tinh,Vu Manh Toi 대한수학회 2018 대한수학회지 Vol.55 No.3
In this paper we consider a class of nonlocal parabolic equations in bounded domains with Dirichlet boundary conditions and a new class of nonlinearities. We first prove the existence and uniqueness of weak solutions by using the compactness method. Then we study the existence and fractal dimension estimates of the global attractor for the continuous semigroup generated by the problem. We also prove the existence of stationary solutions and give a sufficient condition for the uniqueness and global exponential stability of the stationary solution. The main novelty of the obtained results is that no restriction is imposed on the upper growth of the nonlinearities.
Study on the Melting of the Defective Interstitial Alloys TaSi and WSi with BCC Structure
Nguyen Quang Hoc,Tran Dinh Cuong,Bui Duc Tinh,Le Hong Viet 한국물리학회 2019 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.74 No.8
The statistical moment method is used to study the melting of defective interstitial AB alloys, where A is the main element and B is an interstitial atom, with a body-centered-cubic (BCC) structure. The melting temperature of the AB alloy with defects is obtained from the temperature of absolute stability for the crystalline state and the equilibrium vacancy concentration. Numerical calculations are performed for the interstitial alloys TaSi and WSi. Our calculated results are in good agreement with other calculations.
LONG-TIME BEHAVIOR OF A FAMILY OF INCOMPRESSIBLE THREE-DIMENSIONAL LERAY-α-LIKE MODELS
Anh, Cung The,Thuy, Le Thi,Tinh, Le Tran Korean Mathematical Society 2021 대한수학회보 Vol.58 No.5
We study the long-term dynamics for a family of incompressible three-dimensional Leray-α-like models that employ the spectral fractional Laplacian operators. This family of equations interpolates between incompressible hyperviscous Navier-Stokes equations and the Leray-α model when varying two nonnegative parameters 𝜃<sub>1</sub> and 𝜃<sub>2</sub>. We prove the existence of a finite-dimensional global attractor for the continuous semigroup associated to these models. We also show that an operator which projects the weak solution of Leray-α-like models into a finite-dimensional space is determining if it annihilates the difference of two "nearby" weak solutions asymptotically, and if it satisfies an approximation inequality.
Thang Phan,Ha Phan Ai Nguyen,Cao Khoa Dang,Minh Tri Phan,Vu Thanh Nguyen,Van Tuan Le,Binh Thang Tran,Chinh Van Dang,Tinh Huu Ho,Minh Tu Nguyen,Thang Van Dinh,Van Trong Phan,Binh Thai Dang,Huynh Ho Ngo The Korean Society for Preventive Medicine 2023 예방의학회지 Vol.56 No.4
Objectives: The coronavirus disease 2019 (COVID-19) pandemic has increased the workload of healthcare workers (HCWs), impacting their health. This study aimed to assess sleep quality using the Pittsburgh Sleep Quality Index (PSQI) and identify factors associated with poor sleep among HCWs in Vietnam during the COVID-19 pandemic. Methods: In this cross-sectional study, 1000 frontline HCWs were recruited from various healthcare facilities in Vietnam between October 2021 and November 2021. Data were collected using a 3-part self-administered questionnaire, which covered demographics, sleep quality, and factors related to poor sleep. Poor sleep quality was defined as a total PSQI score of 5 or higher. Results: Participants' mean age was 33.20±6.81 years (range, 20.0-61.0), and 63.0% were women. The median work experience was 8.54±6.30 years. Approximately 6.3% had chronic comorbidities, such as hypertension and diabetes mellitus. About 59.5% were directly responsible for patient care and treatment, while 7.1% worked in tracing and sampling. A total of 73.8% reported poor sleep quality. Multivariate logistic regression revealed significant associations between poor sleep quality and the presence of chronic comorbidities (odds ratio [OR], 2.34; 95% confidence interval [CI], 1.17 to 5.24), being a frontline HCW directly involved in patient care and treatment (OR, 1.59; 95% CI, 1.16 to 2.16), increased working hours (OR, 1.84; 95% CI,1.37 to 2.48), and a higher frequency of encountering critically ill and dying patients (OR, 1.42; 95% CI, 1.03 to 1.95). Conclusions: The high prevalence of poor sleep among HCWs in Vietnam during the COVID-19 pandemic was similar to that in other countries. Working conditions should be adjusted to improve sleep quality among this population.