scholarly journals Fractional time stepping and adjoint based gradient computation in an inverse problem for a fractionally damped wave equation

2021 ◽  
pp. 110789
Author(s):  
Barbara Kaltenbacher ◽  
Anna Schlintl
Keyword(s):  
Inverse Problem ◽  
Wave Equation ◽  
Damped Wave Equation ◽  
Time Stepping ◽  
Gradient Computation

An inverse source problem for a damped wave equation with memory

2016 ◽  
Vol 24 (2) ◽  
Author(s):  
Lukáš Šeliga ◽  
Marián Slodička
Keyword(s):  
Inverse Problem ◽  
Wave Equation ◽  
Inverse Source Problem ◽  
Damped Wave Equation ◽  
With Memory

AbstractInverse problem of identifying the unknown spacewise dependent source

scholarly journals Global existence and dynamic structure of solutions for damped wave equation involving the fractional Laplacian

2021 ◽  
Vol 54 (1) ◽  
pp. 245-258
Author(s):  
Younes Bidi ◽  
Abderrahmane Beniani ◽  
Khaled Zennir ◽  
Ahmed Himadan
Keyword(s):  
Wave Equation ◽  
Global Solution ◽  
Fractional Laplacian ◽  
Necessary Conditions ◽  
Dynamic Structure ◽  
Decay Estimates ◽  
Damped Wave Equation ◽  
Structure Of Solutions ◽  
Nonlinear Source ◽  
Galerkin Approximations

Abstract We consider strong damped wave equation involving the fractional Laplacian with nonlinear source. The results of global solution under necessary conditions on the critical exponent are established. The existence is proved by using the Galerkin approximations combined with the potential well theory. Moreover, we showed new decay estimates of global solution.

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