scholarly journals A global unique solvability of entropic weak solution to the one-dimensional pressureless Euler system with a flocking dissipation

2014 ◽  
Vol 257 (5) ◽  
pp. 1333-1371 ◽  
Author(s):  
Seung-Yeal Ha ◽  
Feimin Huang ◽  
Yi Wang
Keyword(s):  
Weak Solution ◽  
Unique Solvability ◽  
Euler System ◽  
One Dimensional ◽  
The One ◽  
Global Unique Solvability

scholarly journals On a stochastic Burgers equation with Dirichlet boundary conditions

2003 ◽  
Vol 2003 (43) ◽  
pp. 2735-2746 ◽  
Author(s):  
Ekaterina T. Kolkovska
Keyword(s):  
Weak Solution ◽  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Burgers Equation ◽  
Martingale Problem ◽  
Weak Limit ◽  
Dirichlet Boundary Conditions ◽  
One Dimensional ◽  
Stochastic Burgers Equation ◽  
The One

We consider the one-dimensional Burgers equation perturbed by a white noise term with Dirichlet boundary conditions and a non-Lipschitz coefficient. We obtain existence of a weak solution proving tightness for a sequence of polygonal approximations for the equation and solving a martingale problem for the weak limit.

The problem of determining the one-dimensional kernel of viscoelasticity equation with a source of explosive type

2020 ◽  
Vol 28 (1) ◽  
pp. 43-52
Author(s):  
Durdimurod Kalandarovich Durdiev ◽  
Zhanna Dmitrievna Totieva
Keyword(s):  
Inverse Problem ◽  
Hyperbolic Equations ◽  
Stability Estimate ◽  
Continuous Functions ◽  
System Of Integral Equations ◽  
One Dimensional ◽  
Weighted Norms ◽  
The Stability ◽  
The One ◽  
Global Unique Solvability

AbstractThe integro-differential system of viscoelasticity equations with a source of explosive type is considered. It is assumed that the coefficients of the equations depend only on one spatial variable. The problem of determining the kernel included in the integral terms of the equations is studied. The solution of the problem is reduced to one inverse problem for scalar hyperbolic equations. This inverse problem is replaced by an equivalent system of integral equations for unknown functions. The principle of constricted mapping in the space of continuous functions with weighted norms to the latter is applied. The theorem of global unique solvability is proved and the stability estimate of solution to the inverse problem is obtained.

GLOBAL WEAK SOLUTIONS OF THE ONE-DIMENSIONAL HYDRODYNAMIC MODEL FOR SEMICONDUCTORS

1993 ◽  
Vol 03 (06) ◽  
pp. 759-788 ◽  
Author(s):  
F. JOCHMANN
Keyword(s):  
Weak Solution ◽  
Viscosity Solutions ◽  
Hydrodynamic Model ◽  
Global Weak Solution ◽  
Limit Problem ◽  
Young Measures ◽  
P System ◽  
Compensated Compactness ◽  
One Dimensional ◽  
The One

The existence of a global weak solution of the one-dimensional hydrodynamic model for semiconductors is proved by the method of artificial viscosity and the theory of compensated compactness. The system is first regularized and global viscosity-solutions are constructed. Letting the viscosity-parameter tend to zero, we obtain a sequence of viscosity-solutions converging in L∞-weak* to a weak solution of the one-dimensional p-system from isoentropic gas dynamics with an electric field term and momentum relaxation. Since the equations are nonlinear and the convergence is only weak, the theory of Young-measures and compensated compactness is applied to obtain a weak solution of the limit problem.

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