scholarly journals On solution of one linear problem with initial and boundary conditions

2021 ◽  
pp. 121
Author(s):  
S.S. Kritskaia
Keyword(s):  
Boundary Conditions ◽  
Boundary Problem ◽  
Fourth Order ◽  
Linear Problem ◽  
Initial Conditions ◽  
Initial And Boundary Conditions

We solve one boundary problem of fourth order with initial conditions, that appears, for example, when one solves the problem about lateral oscillations of elastic-viscous-relaxating rod of variable profile with variable momentum of inertia with freely supported ends.

scholarly journals A nonlinear boundary problem involving thep-bilaplacian operator

2005 ◽  
Vol 2005 (10) ◽  
pp. 1525-1537 ◽  
Author(s):  
Abdelouahed El Khalil ◽  
Siham Kellati ◽  
Abdelfattah Touzani
Keyword(s):  
Boundary Conditions ◽  
Boundary Problem ◽  
Fourth Order ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Conditions ◽  
Nondecreasing Sequence ◽  
Nonlinear Boundary Problem

We show some new Sobolev's trace embedding that we apply to prove that the fourth-order nonlinear boundary conditionsΔp2u+|u|p−2u=0inΩand−(∂/∂n)(|Δu|p−2Δu)=λρ|u|p−2uon∂Ωpossess at least one nondecreasing sequence of positive eigenvalues.

Long-Range Predictability in the Tropics. Part II: 30–60-Day Variability

2005 ◽  
Vol 18 (5) ◽  
pp. 634-650 ◽  
Author(s):  
Thomas Reichler ◽  
John O. Roads
Keyword(s):  
Boundary Conditions ◽  
Long Range ◽  
General Circulation ◽  
Initial Conditions ◽  
Southern Oscillation ◽  
Intraseasonal Variability ◽  
Intraseasonal Oscillation ◽  
Circulation Model ◽  
Lead Times ◽  
Initial And Boundary Conditions

Abstract It is suggested that the slow evolution of the tropical Madden–Julian oscillation (MJO) has the potential to improve the predictability of tropical and extratropical circulation systems at lead times beyond 2 weeks. In practice, however, the MJO phenomenon is extremely difficult to predict because of the lack of good observations, problems with ocean forecasts, and well-known model deficiencies. In this study, the potential skill in forecasting tropical intraseasonal variability is investigated by eliminating all those errors. This is accomplished by conducting five ensemble predictability experiments with a complex general circulation model and by verifying them under the perfect model assumption. The experiments are forced with different combinations of initial and boundary conditions to explore their sensitivity to uncertainties in those conditions. When “perfect” initial and boundary conditions are provided, the model produces a realistic climatology and variability as compared to reanalysis, although the spectral peak of the simulated MJO is too broad. The effect of initial conditions is noticeable out to about 40 days. The quality of the boundary conditions is crucial at all lead times. The small but positive correlations at very long lead times are related to intraseasonal variability of tropical sea surface temperatures (SSTs). When model, initial, and boundary conditions are all perfect, the useful forecast skill of intraseasonal variability is about 4 weeks. Predictability is insensitive to the El Niño–Southern Oscillation (ENSO) phenomenon, but it is enhanced during years when the intraseasonal oscillation is more active. The results provide evidence that the MJO must be understood as a coupled system. As a consequence, it is concluded that further progress in the long-range predictability effort may require the use of fully interactive ocean models.

scholarly journals FORMATION INITIAL AND BOUNDARY CONDITIONS PROBLEM SOLVING EMERGENCY PREVENTION OF NATURAL ORIGIN, CAUSED BY HYDROLOGICAL AND METEOROLOGICAL PHENOMENA IN CERTAIN REGIONS OF THE HIGHLANDS

2020 ◽  
pp. 39-47
Author(s):  
Roman Gudak
Keyword(s):  
Problem Solving ◽  
Boundary Conditions ◽  
Water Saturation ◽  
Initial Conditions ◽  
Sudden Onset ◽  
Information Modeling ◽  
Mountain Area ◽  
Natural Origin ◽  
Base Points ◽  
Initial And Boundary Conditions

Roman Gudak, Serghii Iline, Alexandr Soshinskiy FORMATION INITIAL AND BOUNDARY CONDITIONS PROBLEM SOLVING EMERGENCY PREVENTION OF NATURAL ORIGIN, CAUSED BY HYDROLOGICAL AND METEOROLOGICAL PHENOMENA IN CERTAIN REGIONS OF THE HIGHLANDS Based on a comprehensive analysis of natural and climatic features of the Carpathian region of Ukraine, the initial and boundary conditions for solving the problem of prevention of natural emergencies caused by hydrological and meteorological phenomena in a particular region of the mountain area through the use of rescue helicopters. It is determined that the main feature of the soils of the Carpathian Mountains is their relative looseness and water saturation. With the appearance of additional volumes of aquatic environment, which under the influence of gravity, create significant hydraulic gradients that lead to landslides, mudslides, landslides and races of rivers and streams. Emergencies of a natural nature, which are caused by hydrological and meteorological phenomena, in the mountains have five characteristics. This is the inevitability and sudden onset of a catastrophic event, which can cover a long area, accompanied by great destruction and changes in terrain. Features of emergency management in a particular region of mountainous areas include detailed study of the area and monitoring of local information, geo-information modeling of disasters and early preparation of action plans, constant training of rescuers and preparation for the use of new rescue tools - helicopters. As a result, they form a system of initial and boundary conditions for solving the problem of natural disaster prevention in a particular region of the mountain area, namely: initial conditions for solving the problem - a set of conditions that ensure the fulfillment of orders for delivery to the disaster area and evacuation; boundary conditions - are determined by the maximum load of helicopters, weather conditions, flight time and length of routes, the structure of the graph of the flight task plan and the condition of mandatory return of helicopters to base points. Key words: emergency, mountainous region, helicopter, warning task, initial and boundary conditions

DETERMINISTIC APPROACH TO WATERSHED MODELING

1971 ◽  
Vol 2 (3) ◽  
pp. 146-166 ◽  
Author(s):  
DAVID A. WOOLHISER
Keyword(s):  
Boundary Conditions ◽  
Watershed Modeling ◽  
Deterministic Approach ◽  
Mass Energy ◽  
Deterministic Models ◽  
Conservation Of Mass ◽  
Hydrologic Process ◽  
Theoretical Structure ◽  
Physically Based ◽  
Initial And Boundary Conditions

Physically-based, deterministic models, are considered in this paper. Physically-based, in that the models have a theoretical structure based primarily on the laws of conservation of mass, energy, or momentum; deterministic in the sense that when initial and boundary conditions and inputs are specified, the output is known with certainty. This type of model attempts to describe the structure of a particular hydrologic process and is therefore helpful in predicting what will happen when some change occurs in the system.

DYNAMICS OF THERMAL LOSSES BY CONVECTION AND RADIATION OF THE SPHERICAL HEAT ACCUMULATOR OF SOLAR PLANTS

2020 ◽  
Vol 4 (41) ◽  
pp. 57-62
Author(s):  
SHAVKAT KLYCHEV ◽  
◽  
BAKHRAMOV SAGDULLA ◽  
VALERIY KHARCHENKO ◽  
VLADIMIR PANCHENKO ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Heat Loss ◽  
Initial Conditions ◽  
Water System ◽  
Heat Losses ◽  
Research Purpose ◽  
Heat Accumulator ◽  
Water Heaters ◽  
Intrinsic Radiation ◽  
Over Time

There are needed energy (heat) accumulators to increase the efficiency of solar installations, including solar collectors (water heaters, air heaters, dryers). One of the tasks of designing heat accumulators is to ensure its minimal heat loss. The article considers the problem of determining the distribution of temperatures and heat losses by convection and radiation of the heat insulation-accumulating body (water) system for a ball heat accumulator under symmetric boundary conditions. The problem is solved numerically according to the program developed on the basis of the proposed «gap method». (Research purpose) The research purpose is in determining heat losses by convection and radiation of a two-layer ball heat accumulator with symmetric boundary conditions. (Materials and methods) Authors used the Fourier heat equation for spherical bodies. The article presents the determined boundary and initial conditions for bodies and their surfaces. (Results and discussion) The thickness of the insulation and the volume of the heat accumulator affect the dynamics and values of heat loss. The effect of increasing the thickness of the thermal insulation decreases with increasing its thickness, starting with a certain volume of the heat accumulator or with R > 0.3 meters, the heat losses change almost linearly over time. The dynamics of heat loss decreases with increasing shelf life, but the losses remain large. (Conclusions) Authors have developed a method and program for numerical calculation of heat loss and temperature over time in a spherical two-layer heat accumulator with symmetric boundary conditions, taking into account both falling and intrinsic radiation. The proposed method allows to unify the boundary conditions between contacting bodies.

scholarly journals Solving nonlinear third-order three-point boundary value problems by boundary shape functions methods

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Ji Lin ◽  
Yuhui Zhang ◽  
Chein-Shan Liu
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Initial Conditions ◽  
Boundary Value ◽  
Accurate Solution ◽  
Point Boundary ◽  
Third Order ◽  
Boundary Shape ◽  
Free Function ◽  
New Algorithms

AbstractFor nonlinear third-order three-point boundary value problems (BVPs), we develop two algorithms to find solutions, which automatically satisfy the specified three-point boundary conditions. We construct a boundary shape function (BSF), which is designed to automatically satisfy the boundary conditions and can be employed to develop new algorithms by assigning two different roles of free function in the BSF. In the first algorithm, we let the free functions be complete functions and the BSFs be the new bases of the solution, which not only satisfy the boundary conditions automatically, but also can be used to find solution by a collocation technique. In the second algorithm, we let the BSF be the solution of the BVP and the free function be another new variable, such that we can transform the BVP to a corresponding initial value problem for the new variable, whose initial conditions are given arbitrarily and terminal values are determined by iterations; hence, we can quickly find very accurate solution of nonlinear third-order three-point BVP through a few iterations. Numerical examples confirm the performance of the new algorithms.

scholarly journals Multiple solutions of fourth-order difference equations with different boundary conditions

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Yuhua Long ◽  
Shaohong Wang ◽  
Jiali Chen
Keyword(s):  
Boundary Conditions ◽  
Fourth Order ◽  
Difference Equations ◽  
Multiple Solutions ◽  
Dirichlet Boundary ◽  
Sufficient Conditions ◽  
Dirichlet Boundary Conditions ◽  
Invariant Sets ◽  
Mountain Pass Lemma ◽  
Order Difference

Abstract In the present paper, a class of fourth-order nonlinear difference equations with Dirichlet boundary conditions or periodic boundary conditions are considered. Based on the invariant sets of descending flow in combination with the mountain pass lemma, we establish a series of sufficient conditions on the existence of multiple solutions for these boundary value problems. In addition, some examples are provided to demonstrate the applicability of our results.

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