Global solution of bi-dimensional stochastic equation for a viscous gas

Sludge management is a more and more complex problem due to increased difficulties in locating disposal works and meeting more stringent environmental quality requirements. The most recent notable developments in conventional processing systems have regarded dewatering and stabilization, which remain essential prerequisites to any disposal method. With the increasing pressure on disposal options, such as agricultural use and landfilling, there has been a resurgence of interest in incineration. New processes and alternative uses have been proposed and experienced, but most of them still require further investigations to evaluate effectiveness and reliability. In any case, it is not realistic to search for a global solution to the problem, but the best solutions must derive from local and site-specific considerations.

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e-Navigating in highly-constrained waters: a case study of the Vistula Lagoon

Journal of Navigation ◽

10.1017/s0373463320000661 ◽

2021 ◽

pp. 1-10

Author(s):

Adam Weintrit ◽

Jacek Pietraszkiewicz ◽

Wiesław Piotrzkowski ◽

Wojciech Tycholiz

Keyword(s):

High Resolution ◽

Global Solution ◽

Transition Process ◽

Practical Implementation ◽

Vistula Lagoon ◽

Digital Era ◽

High Resolution Bathymetry ◽

Marine Navigation ◽

The Vistula Lagoon

Abstract In recent years the transition of marine navigation to the digital era has been gaining momentum. Implementation of e-Navigation solutions varies from country to country in terms of their priorities, goals, levels and effects. Maritime authorities in Poland have been setting the pace in this transition process, not only in Poland but also in general as a global solution. The most recent example is the planned deployment of a variety of e-Navigation tools in the Vistula Lagoon: from GNSS-RTK Ground-Based Augmentation System, to virtual and synthetic aids to navigation, high-resolution bathymetry and advanced navigational software for piloting. The major objectives of this paper are, first, to summarise recent dynamics in the e-Navigation field, and second, to present a practical implementation of the e-Navigation concept in the Vistula Lagoon area.

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Global existence and dynamic structure of solutions for damped wave equation involving the fractional Laplacian

Demonstratio Mathematica ◽

10.1515/dema-2021-0022 ◽

2021 ◽

Vol 54 (1) ◽

pp. 245-258

Author(s):

Younes Bidi ◽

Abderrahmane Beniani ◽

Khaled Zennir ◽

Ahmed Himadan

Keyword(s):

Wave Equation ◽

Global Solution ◽

Fractional Laplacian ◽

Necessary Conditions ◽

Dynamic Structure ◽

Decay Estimates ◽

Damped Wave Equation ◽

Structure Of Solutions ◽

Nonlinear Source ◽

Galerkin Approximations

Abstract We consider strong damped wave equation involving the fractional Laplacian with nonlinear source. The results of global solution under necessary conditions on the critical exponent are established. The existence is proved by using the Galerkin approximations combined with the potential well theory. Moreover, we showed new decay estimates of global solution.

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Global well-posedness of the full compressible Hall-MHD equations

Advances in Nonlinear Analysis ◽

10.1515/anona-2020-0178 ◽

2021 ◽

Vol 10 (1) ◽

pp. 1235-1254

Author(s):

Qiang Tao ◽

Canze Zhu

Keyword(s):

Global Solution ◽

Large Time ◽

Initial Temperature ◽

Large Time Behavior ◽

Initial Energy ◽

Mhd Equations ◽

Well Posedness ◽

Time Behavior ◽

Magnetohydrodynamic Flows ◽

Hall Mhd

Abstract This paper deals with a Cauchy problem of the full compressible Hall-magnetohydrodynamic flows. We establish the existence and uniqueness of global solution, provided that the initial energy is suitably small but the initial temperature allows large oscillations. In addition, the large time behavior of the global solution is obtained.

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