scholarly journals Exponential decay for nonlinear abstract evolution equations with a countably infinite number of time‐dependent time delays

2021 ◽  
Author(s):  
Alessandro Paolucci
Keyword(s):  
Exponential Decay ◽  
Infinite Number ◽  
Time Delays ◽  
Evolution Equations ◽  
Time Dependent ◽  
Abstract Evolution Equations ◽  
Countably Infinite

Solvability of the abstract evolution equations in L s -spaces with critical temporal weights

2021 ◽  
Vol 19 (1) ◽  
pp. 111-120
Author(s):  
Qinghua Zhang ◽  
Zhizhong Tan
Keyword(s):  
Cauchy Problem ◽  
Asymptotic Behavior ◽  
Evolution Equation ◽  
Nonlinear Operator ◽  
Evolution Equations ◽  
Bounded Function ◽  
Inhomogeneous Term ◽  
Linear Evolution ◽  
Abstract Evolution Equations ◽  
Linear Evolution Equation

Abstract This paper deals with the abstract evolution equations in L s {L}^{s} -spaces with critical temporal weights. First, embedding and interpolation properties of the critical L s {L}^{s} -spaces with different exponents s s are investigated, then solvability of the linear evolution equation, attached to which the inhomogeneous term f f and its average Φ f \Phi f both lie in an L 1 / s s {L}_{1\hspace{-0.08em}\text{/}\hspace{-0.08em}s}^{s} -space, is established. Based on these results, Cauchy problem of the semi-linear evolution equation is treated, where the nonlinear operator F ( t , u ) F\left(t,u) has a growth number ρ ≥ s + 1 \rho \ge s+1 , and its asymptotic behavior acts like α ( t ) / t \alpha \left(t)\hspace{-0.1em}\text{/}\hspace{-0.1em}t as t → 0 t\to 0 for some bounded function α ( t ) \alpha \left(t) like ( − log t ) − p {\left(-\log t)}^{-p} with 2 ≤ p < ∞ 2\le p\lt \infty .

Free-surface flows with two stagnation points

1996 ◽  
Vol 324 ◽  
pp. 393-406 ◽  
Author(s):  
J.-M. Vanden-Broeck ◽  
F. Dias
Keyword(s):  
Free Surface ◽  
Infinite Number ◽  
Wave Breaking ◽  
Free Surface Flows ◽  
Number Of Solutions ◽  
Surface Flows ◽  
Stagnation Points ◽  
Surface Profiles ◽  
Countably Infinite

Symmetric suction flows are computed. The flows are free-surface flows with two stagnation points. The configuration is related to the modelling of wave breaking at the bow of a ship. It is shown that there is a countably infinite number of solutions and that the free-surface profiles are characterized by waves.

scholarly journals LINEAR TIME-DEPENDENT INVARIANTS FOR SCALAR FIELDS AND NOETHER’S THEOREM

1994 ◽  
Vol 09 (19) ◽  
pp. 1785-1790 ◽  
Author(s):  
O. CASTAÑOS ◽  
R. LÓPEZ-PEÑA ◽  
V.I. MAN’KO
Keyword(s):  
Scalar Field ◽  
Infinite Number ◽  
Linear Time ◽  
Scalar Fields ◽  
Time Dependent ◽  
Noether’S Theorem ◽  
Noether's Theorem

The infinite number of time-dependent linear in field and conjugated momenta invariants is derived for the scalar field using the Noether’s theorem procedure.

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