scholarly journals An identification problem for a linear evolution equation in a Banach space and applications

2011 ◽  
Vol 4 (3) ◽  
pp. 671-691 ◽  
Author(s):  
Alfredo Lorenzi ◽  
◽  
Ioan I. Vrabie ◽  
Keyword(s):  
Banach Space ◽  
Evolution Equation ◽  
Identification Problem ◽  
Linear Evolution ◽  
Linear Evolution Equation

scholarly journals An identification problem for a linear evolution equation in a banach space

2018 ◽  
Vol 0 (0) ◽  
pp. 1-12
Author(s):  
Viorel Barbu ◽  
◽  
Gabriela Marinoschi ◽  
Keyword(s):  
Banach Space ◽  
Evolution Equation ◽  
Identification Problem ◽  
Linear Evolution ◽  
Linear Evolution Equation

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 .

Infinitely many lie-bäcklund symmetries for a quasi-linear evolution equation

1982 ◽  
Vol 90 (4) ◽  
pp. 159-161 ◽  
Author(s):  
K.M. Tamizhmani ◽  
M. Lakshmanan
Keyword(s):  
Evolution Equation ◽  
Linear Evolution ◽  
Linear Evolution Equation

An example of a non-linear evolution equation showing ‘chaos-enhancement’

1979 ◽  
Vol 3 (6) ◽  
pp. 463-465 ◽  
Author(s):  
B. Crell ◽  
A. Uhlmann
Keyword(s):  
Evolution Equation ◽  
Linear Evolution ◽  
Linear Evolution Equation ◽  
Non Linear

Modified dissipativity for a non-linear evolution equation arising in turbulence

1979 ◽  
Vol 71 (3) ◽  
pp. 237-256 ◽  
Author(s):  
C. Bardos ◽  
P. Penel ◽  
U. Frisch ◽  
P. L. Sulem
Keyword(s):  
Evolution Equation ◽  
Linear Evolution ◽  
Linear Evolution Equation ◽  
Non Linear
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