On the global solubility of the Cauchy problem for hyperbolic Monge–Ampére systems

2018 ◽  
Vol 82 (5) ◽  
pp. 1019-1075 ◽  
Author(s):  
D. V. Tunitsky
Keyword(s):  
Cauchy Problem ◽  
The Cauchy Problem ◽  
Monge Ampere

Entire Solutions of Cauchy Problem for Parabolic Monge–Ampère Equations

2020 ◽  
Vol 20 (4) ◽  
pp. 769-781
Author(s):  
Limei Dai ◽  
Jiguang Bao
Keyword(s):  
Cauchy Problem ◽  
Asymptotic Behavior ◽  
Viscosity Solutions ◽  
Existence And Uniqueness ◽  
Entire Solutions ◽  
Perron Method ◽  
The Cauchy Problem ◽  
Monge Ampere

AbstractIn this paper, we study the Cauchy problem of the parabolic Monge–Ampère equation-u_{t}\det D^{2}u=f(x,t)and obtain the existence and uniqueness of viscosity solutions with asymptotic behavior by using the Perron method.

scholarly journals The Cauchy problem for the homogeneous Monge–Ampère equation, III. Lifespan

2017 ◽  
Vol 2017 (724) ◽  
Author(s):  
Yanir A. Rubinstein ◽  
Steve Zelditch
Keyword(s):  
Cauchy Problem ◽  
A Priori ◽  
Complex Domain ◽  
Regularity Conditions ◽  
Uniqueness Of Solutions ◽  
The Real ◽  
Homogeneous Complex ◽  
The Cauchy Problem ◽  
Complex Settings ◽  
Monge Ampere

AbstractWe prove several results on the lifespan, regularity, and uniqueness of solutions of the Cauchy problem for the homogeneous complex and real Monge–Ampère equations (HCMA/HRMA) under various a priori regularity conditions. We use methods of characteristics in both the real and complex settings to bound the lifespan of solutions with prescribed regularity. In the complex domain, we characterize the

Cauchy Problem for Equations with Fractional Differentiation Bessel Operator in the Space of Temperate Distributions

2003 ◽  
Vol 8 (1) ◽  
pp. 61-75
Author(s):  
V. Litovchenko
Keyword(s):  
Functional Analysis ◽  
Cauchy Problem ◽  
Fundamental Solution ◽  
Initial Function ◽  
Well Posedness ◽  
Fractional Differentiation ◽  
Basic Tool ◽  
Conjugate Space ◽  
Analysis Technique ◽  
The Cauchy Problem

The well-posedness of the Cauchy problem, mentioned in title, is studied. The main result means that the solution of this problem is usual C∞ - function on the space argument, if the initial function is a real functional on the conjugate space to the space, containing the fundamental solution of the corresponding problem. The basic tool for the proof is the functional analysis technique.

Fundamental Serrin type regularity criteria for 3D MHD fluid passing through the porous medium

Filomat ◽  
2017 ◽  
Vol 31 (5) ◽  
pp. 1287-1293 ◽  
Author(s):  
Zujin Zhang ◽  
Dingxing Zhong ◽  
Shujing Gao ◽  
Shulin Qiu
Keyword(s):  
Cauchy Problem ◽  
Porous Medium ◽  
Regularity Criterion ◽  
Regularity Criteria ◽  
The Cauchy Problem ◽  
Appl Math

In this paper, we consider the Cauchy problem for the 3D MHD fluid passing through the porous medium, and provide some fundamental Serrin type regularity criteria involving the velocity or its gradient, the pressure or its gradient. This extends and improves [S. Rahman, Regularity criterion for 3D MHD fluid passing through the porous medium in terms of gradient pressure, J. Comput. Appl. Math., 270 (2014), 88-99].

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