scholarly journals The Cauchy–Neumann and Cauchy–Robin problems for a class of hyperbolic operators with double characteristics in presence of transition

2020 ◽  
Vol 11 (4) ◽  
pp. 1991-2022
Author(s):  
Annamaria Barbagallo ◽  
Vincenzo Esposito
Keyword(s):  
Sobolev Spaces ◽  
Existence And Uniqueness ◽  
A Priori Estimates ◽  
A Priori ◽  
Existence And Uniqueness Results ◽  
Mixed Problems ◽  
Uniqueness Results ◽  
Hyperbolic Operators ◽  
Priori Estimates

Abstract The mixed Cauchy–Neumann and Cauchy–Robin problems for a class of hyperbolic operators with double characteristics in presence of transition is investigated. Some a priori estimates in Sobolev spaces with negative indexes are proved. Subsequently, existence and uniqueness results for the mixed problems are obtained.

scholarly journals On nonlocal minimal graphs

2021 ◽  
Vol 60 (4) ◽  
Author(s):  
Matteo Cozzi ◽  
Luca Lombardini
Keyword(s):  
Existence And Uniqueness ◽  
A Priori Estimates ◽  
A Priori ◽  
Analytic Approach ◽  
Comparison Principles ◽  
Minimal Graphs ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Priori Estimates ◽  
Rearrangement Inequalities

AbstractWe develop a functional analytic approach for the study of nonlocal minimal graphs. Through this, we establish existence and uniqueness results, a priori estimates, comparison principles, rearrangement inequalities, and the equivalence of several notions of minimizers and solutions.

scholarly journals On the Cauchy problem for a class of hyperbolic operators with triple characteristics

2020 ◽  
Author(s):  
Annamaria Barbagallo ◽  
Vincenzo Esposito
Keyword(s):  
Cauchy Problem ◽  
Sobolev Spaces ◽  
Existence Result ◽  
A Priori Estimates ◽  
A Priori ◽  
Hyperbolic Operators ◽  
Priori Estimates ◽  
The Cauchy Problem

AbstractThe Cauchy problem for a class of hyperbolic operators with triple characteristics is analyzed. Some a priori estimates in Sobolev spaces with negative indexes are proved. Subsequently, an existence result for the Cauchy problem is obtained.

A priori estimates in Sobolev spaces for a class of hyperbolic operators in presence of transition

2019 ◽  
Vol 16 (02) ◽  
pp. 245-270 ◽  
Author(s):  
Annamaria Barbagallo ◽  
Vincenzo Esposito
Keyword(s):  
Sobolev Spaces ◽  
A Priori Estimates ◽  
A Priori ◽  
Second Order ◽  
Hyperbolic Operators ◽  
Priori Estimates ◽  
Euclidian Space ◽  
Global Nature

We establish several a priori estimates of local or global nature in Sobolev spaces with general exponent [Formula: see text] for a class of second-order hyperbolic operators with double characteristics in presence of a transition in a domain of the Euclidian space [Formula: see text].

scholarly journals Boundary value problems with nonlocal conditions for hyperbolic systems of equations with two independent variables

2020 ◽  
Vol 53 (2) ◽  
pp. 159-180
Author(s):  
V. M. Kyrylych ◽  
O. Z. Slyusarchuk
Keyword(s):  
Boundary Value Problems ◽  
A Priori Estimates ◽  
Hyperbolic Systems ◽  
Boundary Value ◽  
A Priori ◽  
Nonlocal Boundary ◽  
Nonlocal Conditions ◽  
Mixed Problems ◽  
Priori Estimates ◽  
Smooth Coefficients

Nonlocal boundary value problems for arbitrary order hyperbolic systems with one spatial variable are considered. A priori estimates for general nonlocal mixed problems for systems with smooth and piecewise smooth coefficients are obtained. The correct solvability of such problems is proved.Examples of additional conditions necessity are provided.

A difference scheme for equations of ocean dynamics on unstructured grids

2014 ◽  
Vol 29 (3) ◽  
Author(s):  
Alexey V. Drutsa
Keyword(s):  
Difference Scheme ◽  
Existence And Uniqueness ◽  
Large Scale ◽  
A Priori Estimates ◽  
Unstructured Grids ◽  
A Priori ◽  
Ocean Dynamics ◽  
Priori Estimates ◽  
Uniqueness Of The Solution ◽  
Grid Operators

AbstractA difference scheme on unstructured grids is constructed for the system of equations of large scale ocean dynamics. The properties of the grid problem and grid operators are studied, in particular, a series of a priori estimates and the theorem on existence and uniqueness of the solution are proved.

On Approximations to Solutions of Nonlinear Integral Equations of the Urysohn Type

1973 ◽  
Vol 16 (1) ◽  
pp. 137-141
Author(s):  
K. A. Zischka
Keyword(s):  
Existence And Uniqueness ◽  
A Priori Estimates ◽  
A Priori ◽  
Sufficient Conditions ◽  
Successive Approximations ◽  
Uniqueness Of Solutions ◽  
Nonlinear Integral Equations ◽  
Priori Estimates ◽  
The Given ◽  
Uniqueness Of A Solution

This note will derive a priori estimates of the errors due to replacing the given integral operator A by a similar operator A* of the same type when successive approximations are applied to the integral equation φ=Aφ.The existence and uniqueness of solutions to this equation follow easily by applying a well known fixed point theorem in a Banach space to the above mapping [1, 2]. Moreover, sufficient conditions for the existence and uniqueness of a solution to Urysohn's equation are stated explicitly in a note by the author [3].

ASYMPTOTIC BEHAVIOR OF STOCHASTIC DISSIPATIVE QUANTUM ZAKHAROV EQUATIONS

2013 ◽  
Vol 13 (02) ◽  
pp. 1250016 ◽  
Author(s):  
YANFENG GUO ◽  
BOLING GUO ◽  
DONGLONG LI
Keyword(s):  
Asymptotic Behavior ◽  
White Noise ◽  
Approximation Method ◽  
Existence And Uniqueness ◽  
A Priori Estimates ◽  
A Priori ◽  
Galerkin Approximation ◽  
Uniqueness Of Solutions ◽  
Asymptotic Behaviors ◽  
Priori Estimates

The stochastic dissipative quantum Zakharov equations with white noise are studied. The existence and uniqueness of solutions are obtained by using the standard Galerkin approximation method on the basis of the time uniform a priori estimates in various spaces. Moreover, the asymptotic behaviors of the solutions for the stochastic dissipative quantum Zakharov equations with white noise are also investigated.

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