Optimal control of wave propagation governed by nonlinear partial differential equations

1997 ◽  
Author(s):  
Vladimir Khasilev
Keyword(s):  
Optimal Control ◽  
Wave Propagation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Partial Differential

scholarly journals Analytical mathematical schemes: Circular rod grounded via transverse Poisson’s effect and extensive wave propagation on the surface of water

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 545-554
Author(s):  
Asghar Ali ◽  
Aly R. Seadawy ◽  
Dumitru Baleanu
Keyword(s):  
Wave Propagation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Longitudinal Wave ◽  
Symbolic Computation ◽  
Boussinesq Equation ◽  
Nonlinear Partial Differential Equations ◽  
Wave Model ◽  
Simple Equation ◽  
Partial Differential

AbstractThis article scrutinizes the efficacy of analytical mathematical schemes, improved simple equation and exp(-\text{Ψ}(\xi ))-expansion techniques for solving the well-known nonlinear partial differential equations. A longitudinal wave model is used for the description of the dispersion in the circular rod grounded via transverse Poisson’s effect; similarly, the Boussinesq equation is used for extensive wave propagation on the surface of water. Many other such types of equations are also solved with these techniques. Hence, our methods appear easier and faster via symbolic computation.

scholarly journals The Classical Continuous Mixed Optimal Control of Couple Nonlinear Parabolic Partial Differential Equations with State Constraints

2021 ◽  
pp. 4859-4874
Author(s):  
Jamil A Ali Al-Hawasy ◽  
Ghufran M Kadhem ◽  
Ahmed Abdul Hasan Naeif
Keyword(s):  
Optimal Control ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
State Constraints ◽  
Nonlinear Partial Differential Equations ◽  
Parabolic Partial Differential Equations ◽  
Control Vector ◽  
Partial Differential ◽  
Vector Solution ◽  
Nonlinear Parabolic

In this work, the classical continuous mixed optimal control vector (CCMOPCV) problem of couple nonlinear partial differential equations of parabolic (CNLPPDEs) type with state constraints (STCO) is studied. The existence and uniqueness theorem (EXUNTh) of the state vector solution (SVES) of the CNLPPDEs for a given CCMCV is demonstrated via the method of Galerkin (MGA). The EXUNTh of the CCMOPCV ruled with the CNLPPDEs is proved. The Frechet derivative (FÉDE) is obtained. Finally, both the necessary and the sufficient theorem conditions for optimality (NOPC and SOPC) of the CCMOPCV with state constraints (STCOs) are proved through using the Kuhn-Tucker-Lagrange (KUTULA) multipliers theorem (KUTULATH).

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