Lp estimates of solutions to certain hyperbolic equations

1988 ◽  
Vol 39 (4) ◽  
pp. 365-370
Author(s):  
A. I. Markovskii
Keyword(s):  
Hyperbolic Equations ◽  
Lp Estimates ◽  
Estimates Of Solutions

scholarly journals On some Lp-estimates for hyperbolic equations

1992 ◽  
Vol 30 (1-2) ◽  
pp. 149-163 ◽  
Author(s):  
Mitsuru Sugimoto
Keyword(s):  
Hyperbolic Equations ◽  
Lp Estimates

scholarly journals Lp - estimates of solutions of backward doubly stochastic differential equations

Filomat ◽  
2017 ◽  
Vol 31 (8) ◽  
pp. 2365-2379
Author(s):  
Jasmina Djordjevic
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Large Class ◽  
General Type ◽  
Lp Estimates ◽  
Estimates Of Solutions ◽  
Doubly Stochastic ◽  
Lipschitz Conditions

This paper deals with a large class of nonhomogeneous backward doubly stochastic differential equations which have a more general form of the forward It? integrals. Terms under which the solutions of these equations are bounded in the Lp-sense, p ? 2, under both the Lipschitz and non-Lipschitz conditions, are given, i.e. Lp - stability for this general type of backward doubly stochastic differential equations is established.

scholarly journals A Navier–Stokes-Type Problem with High-Order Elliptic Operator and Applications

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2256
Author(s):  
Maria Alessandra Ragusa ◽  
Veli B. Shakhmurov
Keyword(s):  
Banach Space ◽  
Mixed Problem ◽  
Stokes Equations ◽  
Stokes Problem ◽  
High Order ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Lp Estimates ◽  
Estimates Of Solutions ◽  
Order Elliptic Operator

The existence, uniqueness and uniformly Lp estimates for solutions of a high-order abstract Navier–Stokes problem on half space are derived. The equation involves an abstract operator in a Banach space E and small parameters. Since the Banach space E is arbitrary and A is a possible linear operator, by choosing spaces E and operators A, the existence, uniqueness and Lp estimates of solutions for numerous classes of Navier–Stokes type problems are obtained. In application, the existence, uniqueness and uniformly Lp estimates for the solution of the Wentzell–Robin-type mixed problem for the Navier–Stokes equation and mixed problem for degenerate Navier–Stokes equations are established.

scholarly journals An Optimal Control Problem by a Hybrid System of Hyperbolic and Ordinary Differential Equations

Games ◽  
2021 ◽  
Vol 12 (1) ◽  
pp. 23
Author(s):  
Alexander Arguchintsev ◽  
Vasilisa Poplevko
Keyword(s):  
Optimal Control ◽  
Differential Equations ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Ordinary Differential Equations ◽  
Hyperbolic Equations ◽  
Control Methods ◽  
The Right ◽  
The Cost ◽  
Optimal Control Methods

This paper deals with an optimal control problem for a linear system of first-order hyperbolic equations with a function on the right-hand side determined from controlled bilinear ordinary differential equations. These ordinary differential equations are linear with respect to state functions with controlled coefficients. Such problems arise in the simulation of some processes of chemical technology and population dynamics. Normally, general optimal control methods are used for these problems because of bilinear ordinary differential equations. In this paper, the problem is reduced to an optimal control problem for a system of ordinary differential equations. The reduction is based on non-classic exact increment formulas for the cost-functional. This treatment allows to use a number of efficient optimal control methods for the problem. An example illustrates the approach.

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