scholarly journals On Initial Boundary Value Problem for Parabolic Differential Operator with Non-coercive Boundary Conditions

2020 ◽  
pp. 547-558
Author(s):  
Alexander N. Polkovnikov
Keyword(s):  
Differential Operator ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Sobolev Type ◽  
Type Spaces ◽  
Bochner Space ◽  
Initial Boundary Value

We consider initial boundary value problem for uniformly 2-parabolic differential operator of second order in cylinder domain in Rn with non-coercive boundary conditions. In this case there is a loss of smoothness of the solution in Sobolev type spaces compared with the coercive situation. Using by Faedo-Galerkin method we prove that problem has unique solution in special Bochner space

scholarly journals ON A 3D INITIAL-BOUNDARY VALUE PROBLEM FOR DETERMINING THE DYNAMICS OF IMPURITIES CONCENTRATION IN A HORIZONTAL LAYERED FINE-PORE MEDIUM

2019 ◽  
Vol 3 ◽  
pp. 60
Author(s):  
Sharif E. Guseynov ◽  
Ruslans Aleksejevs ◽  
Jekaterina V. Aleksejeva
Keyword(s):  
Parabolic Equation ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Analytical Approach ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Unsteady State ◽  
State Boundary ◽  
Initial Boundary Value

In the present paper, we propose an analytical approach for solving the 3D unsteady-state boundary-value problem for the second-order parabolic equation with the second and third types boundary conditions in two-layer rectangular parallelepipedic domain.

Definitions of solutions to the IBVP for multi-dimensional scalar balance laws

2018 ◽  
Vol 15 (02) ◽  
pp. 349-374 ◽  
Author(s):  
Elena Rossi
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
General Framework ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Balance Laws ◽  
Initial Boundary Value

We consider four definitions of solution to the initial-boundary value problem (IBVP) for a scalar balance laws in several space dimensions. These definitions are extended to the same most general framework and then compared. The first aim of this paper is to detail differences and analogies among them. We focus then on the ways the boundary conditions are fulfilled according to each definition, providing also connections among these various modes. The main result is the proof of the equivalence among the presented definitions of solution.

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