scholarly journals Unique solvability of a nonlinear thermoviscoelasticity system in Sobolev space with a mixed norm

2011 ◽  
Vol 4 (2) ◽  
pp. 441-466 ◽  
Author(s):  
Irena Pawłow ◽  
◽  
Wojciech M. Zajączkowski ◽  
Keyword(s):  
Sobolev Space ◽  
Unique Solvability ◽  
Mixed Norm ◽  
Nonlinear Thermoviscoelasticity

On a Spatial Problem of Darboux Type for a Second-Order Hyperbolic Equation

1995 ◽  
Vol 2 (3) ◽  
pp. 299-311
Author(s):  
S. Kharibegashvili
Keyword(s):  
Sobolev Space ◽  
Hyperbolic Equation ◽  
Unique Solvability ◽  
Second Order ◽  
Spatial Problem ◽  
Order Hyperbolic Equation ◽  
Second Order Hyperbolic Equation

Abstract The theorem of unique solvability of a spatial problem of Darboux type in Sobolev space is proved for a second-order hyperbolic equation.

scholarly journals Weighted Norm Inequalities for Multilinear Fourier Multipliers with Mixed Norm

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Mai Fujita
Keyword(s):  
Sobolev Space ◽  
Fourier Multipliers ◽  
Mixed Norm ◽  
Weighted Norm ◽  
Weighted Norm Inequalities ◽  
Norm Inequalities ◽  
Sobolev Regularity

In this paper, weighted norm inequalities for multilinear Fourier multipliers satisfying Sobolev regularity with mixed norm are discussed. Our result can be understood as a generalization of the result by Fujita and Tomita by using the L r -based Sobolev space, 1 < r ≤ 2 with mixed norm.

On the Prandtl Equation

1999 ◽  
Vol 6 (6) ◽  
pp. 525-536
Author(s):  
R. Duduchava ◽  
D. Kapanadze
Keyword(s):  
Differential Equation ◽  
Sobolev Space ◽  
Unique Solvability ◽  
Bessel Potential ◽  
Integro Differential Equation ◽  
Prandtl Equation ◽  
Bessel Potential Spaces

Abstract The unique solvability of the airfoil (Prandtl) integro-differential equation on the semi-axis is proved in the Sobolev space and Bessel potential spaces under certain restrictions on 𝑝 and 𝑠.

scholarly journals A PROBLEM ON VIBRATION OF A BAR WITH UNKNOWN BOUNDARY CONDITION ON A PART OF THE BOUNDARY

2017 ◽  
Vol 23 (2) ◽  
pp. 7-14
Author(s):  
A. B. Beylin ◽  
L. S. Pulkina
Keyword(s):  
Boundary Condition ◽  
Inverse Problem ◽  
Sobolev Space ◽  
Unique Solvability ◽  
A Priori Estimates ◽  
A Priori ◽  
The Other ◽  
Unknown Boundary ◽  
Priori Estimates ◽  
The Subject

In this paper, we study an inverse problem for hyperbolic equation. This problem arises when we consider vibration of a nonhomogeneous bar if one endpoint is fixed by spring but behavior of the other is unknown and is the subject to find. Overdetermination is given in the form of integral with respect to spacial variable. Unique solvability of this problem is proved under some conditions on data. The proof is based on a priori estimates in Sobolev space.

scholarly journals ON A CERTAIN PROBLEM FOR A WAVE EQUATION

2017 ◽  
Vol 17 (5) ◽  
pp. 12-17
Author(s):  
S.A. Beilin
Keyword(s):  
Wave Equation ◽  
Sobolev Space ◽  
Hyperbolic Equation ◽  
Unique Solvability ◽  
Classical Boundary

In this paper a hyperbolic equation with non-classical boundary conditionsfor a hyperbolic equation is studied. This problem can be viewed as the generalization of the problem about the oscillation of the string if it ends experiencethe resistance of medium. The unique solvability of the problem is proved. Theprove of solvability is based on the received a priory estimates in Sobolev space.

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