scholarly journals MAXIMAL REGULARITY ESTIMATE FOR A DIFFERENTIAL EQUATION WITH OSCILLATING COEFFICIENTS

2021 ◽  
Vol 109 (1) ◽  
Author(s):  
A. N. Yesbayev ◽  
K. N. Ospanov
Keyword(s):  
Differential Equation ◽  
Maximal Regularity ◽  
Regularity Estimate ◽  
Oscillating Coefficients

scholarly journals Lorentz spaces in action on pressureless systems arising from models of collective behavior

2021 ◽  
Author(s):  
Raphaël Danchin ◽  
Piotr Bogusław Mucha ◽  
Patrick Tolksdorf
Keyword(s):  
Initial Data ◽  
Collective Behavior ◽  
Existence And Uniqueness ◽  
Maximal Regularity ◽  
Parabolic Systems ◽  
Lorentz Spaces ◽  
Regularity Estimate ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Time Existence

AbstractWe are concerned with global-in-time existence and uniqueness results for models of pressureless gases that come up in the description of phenomena in astrophysics or collective behavior. The initial data are rough: in particular, the density is only bounded. Our results are based on interpolation and parabolic maximal regularity, where Lorentz spaces play a key role. We establish a novel maximal regularity estimate for parabolic systems in $$L_{q,r}(0,T;L_p(\Omega ))$$ L q , r ( 0 , T ; L p ( Ω ) ) spaces.

scholarly journals Oscillation for advanced differential equations with oscillating coefficients

2003 ◽  
Vol 2003 (33) ◽  
pp. 2109-2118 ◽  
Author(s):  
Xianyi Li ◽  
Deming Zhu ◽  
Hanqing Wang
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Positive Constant ◽  
Sufficient Conditions ◽  
All Solutions ◽  
Oscillating Coefficients ◽  
T Tau

Some sufficient conditions are established for the oscillation of all solutions of the advanced differential equationx′(t)−p(t)x(t+τ)=0,t≥t0, where the coefficientp(t)∈C([t0,∞),R)is oscillatory, andτis a positive constant.

scholarly journals Oscillation and nonoscillation of a delay differential equation

1994 ◽  
Vol 49 (1) ◽  
pp. 69-79 ◽  
Author(s):  
Chunhai Kou ◽  
Weiping Yan ◽  
Jurang Yan
Keyword(s):  
Differential Equation ◽  
Delay Differential Equation ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
First Order ◽  
Oscillating Coefficients ◽  
Image Position ◽  
Delay Differential ◽  
Necessary And Sufficient ◽  
Oscillation And Nonoscillation

In this paper, some necessary and sufficient conditions for oscillation of a first order delay differential equation with oscillating coefficients of the formare established. Several applications of our results improve and generalise some of the known results in the literature.

Asymptotic solution of the Cauchy problem for the singularly perturbed partial integro-differential equation with rapidly oscillating coefficients and with rapidly oscillating heterogeneity

2021 ◽  
Vol 19 (1) ◽  
pp. 244-258
Author(s):  
Burkhan T. Kalimbetov ◽  
Olim D. Tuychiev
Keyword(s):  
Differential Equation ◽  
Cauchy Problem ◽  
Asymptotic Solution ◽  
Regularization Method ◽  
Singularly Perturbed ◽  
New Approach ◽  
The Cauchy Problem ◽  
Oscillating Coefficients ◽  
Oscillating Coefficient ◽  
The Relationship

Abstract In this paper, the regularization method of S. A. Lomov is generalized to integro-differential equations with rapidly oscillating coefficients and with a rapidly oscillating right-hand side. The main goal of the work is to reveal the influence of the oscillating components on the structure of the asymptotics of the solution of this problem. The case of coincidence of the frequencies of a rapidly oscillating coefficient and a rapidly oscillating inhomogeneity is considered. In this case, only the identical resonance is observed in the problem. Other cases of the relationship between frequencies can lead to so-called non-identical resonances, the study of which is nontrivial and requires the development of a new approach. It is supposed to study these cases in our further work.

scholarly journals Resolution in hölder spaces of an elliptic problem in an unbounded domain

2006 ◽  
Vol 81 (3) ◽  
pp. 387-404 ◽  
Author(s):  
Tarik Berroug ◽  
Rabah Labbas ◽  
Boubaker-Khaled Sadallah
Keyword(s):  
Differential Equation ◽  
Continuous Function ◽  
Boundary Conditions ◽  
Unbounded Domain ◽  
Elliptic Problem ◽  
Order Differential Equation ◽  
Maximal Regularity ◽  
Hölder Continuous ◽  
Strict Solution ◽  
The Right

AbstractIn this paper we give new results concerning the maximal regularity of the strict solution of an abstract second-order differential equation, with non-homogeneous boundary conditions of Dirichlet type, and set in an unbounded interval. The right-hand term of the equation is a Hölder continuous function.

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