Dirichlet Type Problems for First Order Strictly Hyperbolic Systems with Constant Coefficients in a Two-Dimensional Domain

2019 ◽  
Vol 237 (4) ◽  
pp. 595-609
Author(s):  
N. A. Zhura ◽  
V. A. Polunin
Keyword(s):  
Hyperbolic Systems ◽  
Two Dimensional ◽  
First Order ◽  
Dirichlet Type ◽  
Constant Coefficients ◽  
Dimensional Domain

Evaluation of a Two-Dimensional Conductivity Function Based on Boundary Measurements

1999 ◽  
Vol 122 (2) ◽  
pp. 367-371 ◽  
Author(s):  
M. Tadi
Keyword(s):  
Optimal Estimation ◽  
Two Dimensional ◽  
Zeroth Order ◽  
First Order ◽  
Conductivity Profile ◽  
Boundary Measurements ◽  
Conductivity Function ◽  
The Given ◽  
Close Estimate ◽  
Dimensional Domain

This paper is concerned with an inverse problem for the conduction of heat in a two-dimensional domain. It seeks to recover the subsurface conductivity profile based on the measurements obtained at the boundary. The method considers a temporal interval for which time-dependent measurements are provided. It formulates an optimal estimation problem which seeks to minimize the error difference between the given data and the response from the system. It uses a combination of the zeroth-order and the first-order Tikhonov regularization to stabilize the inversion. The method leads to an iterative algorithm which, at every iteration, requires the solution to a two-point boundary value problem. A number of numerical results are presented which indicate that a close estimate of the thermal conductivity function can be obtained based on the boundary measurements only. [S0022-1481(00)00902-6]

scholarly journals Solving puzzles in deformed JT gravity: phase transitions and non-perturbative effects

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Clifford V. Johnson ◽  
Felipe Rosso
Keyword(s):  
Phase Structure ◽  
Scalar Potential ◽  
String Equation ◽  
Two Dimensional ◽  
Leading Order ◽  
Classical Analysis ◽  
First Order ◽  
First Order Phase Transition ◽  
Definition Of ◽  
First Order Phase

Abstract Recent work has shown that certain deformations of the scalar potential in Jackiw-Teitelboim gravity can be written as double-scaled matrix models. However, some of the deformations exhibit an apparent breakdown of unitarity in the form of a negative spectral density at disc order. We show here that the source of the problem is the presence of a multi-valued solution of the leading order matrix model string equation. While for a class of deformations we fix the problem by identifying a first order phase transition, for others we show that the theory is both perturbatively and non-perturbatively inconsistent. Aspects of the phase structure of the deformations are mapped out, using methods known to supply a non-perturbative definition of undeformed JT gravity. Some features are in qualitative agreement with a semi-classical analysis of the phase structure of two-dimensional black holes in these deformed theories.

On the Boundary Value Problem in A Dihedral Angle for Normally Hyperbolic Systems of First Order

1998 ◽  
Vol 5 (2) ◽  
pp. 121-138
Author(s):  
O. Jokhadze
Keyword(s):  
Partial Differential Equations ◽  
Boundary Value Problem ◽  
Principal Part ◽  
Hyperbolic Systems ◽  
Boundary Value ◽  
Three Dimensional ◽  
Order System ◽  
First Order ◽  
Dimensional Boundary ◽  
Class Of Functions

Abstract Some structural properties as well as a general three-dimensional boundary value problem for normally hyperbolic systems of partial differential equations of first order are studied. A condition is given which enables one to reduce the system under consideration to a first-order system with the spliced principal part. It is shown that the initial problem is correct in a certain class of functions if some conditions are fulfilled.

Partially Invariant Solutions for Two-dimensional Ideal MHD Equations

1990 ◽  
Vol 45 (11-12) ◽  
pp. 1219-1229 ◽  
Author(s):  
D.-A. Becker ◽  
E. W. Richter
Keyword(s):  
Differential Equations ◽  
Linear Equations ◽  
Mhd Equations ◽  
Two Dimensional ◽  
Invariant Solutions ◽  
First Order ◽  
Partially Invariant Solutions ◽  
Quasilinear Systems ◽  
Ideal Mhd ◽  
Non Linear Equations

AbstractA generalization of the usual method of similarity analysis of differential equations, the method of partially invariant solutions, was introduced by Ovsiannikov. The degree of non-invariance of these solutions is characterized by the defect of invariance d. We develop an algorithm leading to partially invariant solutions of quasilinear systems of first-order partial differential equations. We apply the algorithm to the non-linear equations of the two-dimensional non-stationary ideal MHD with a magnetic field perpendicular to the plane of motion.

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