The problem of control of a two-dimensional transformation of spatial arguments in a parabolic functional-differential equation

DOI10.1134/S001226610608009XzbMath1140.35472OpenAlexW1972359478WikidataQ115253500 ScholiaQ115253500MaRDI QIDQ2480416

A. V. Razgulin

Publication date: 31 March 2008

Published in: Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s001226610608009x

zbMATH Keywords

nonlinear optical systemsnonlocal feedbackuniform quasidifferentiability of the objective functional

Mathematics Subject Classification ID

Optimality conditions for problems involving partial differential equations (49K20) Newton-type methods (49M15) Smoothness and regularity of solutions to PDEs (35B65) Nonlinear parabolic equations (35K55) Partial functional-differential equations (35R10)

Related Items (11)

Optimal control of nonlinear evolution systems in the case where the solution is not differentiable with respect to the control ⋮ Rotating waves in parabolic functional differential equations with rotation of spatial argument and time delay ⋮ Classical solutions of hyperbolic differential-difference equations in a half-space ⋮ On the matrix Fourier filtering problem for a class of models of nonlinear optical systems with a feedback ⋮ Boundary value problems for functional differential canonical equations of mixed type ⋮ Dynamics of stationary structures in a parabolic problem with reflected spatial argument ⋮ Rotating Waves in a Model of Delayed Feedback Optical System with Diffraction ⋮ Two-dimensional rotating waves in a functional-differential diffusion equation with rotation of spatial arguments and time delay ⋮ Stable structures of nonlinear parabolic equations with transformation of spatial variables ⋮ Boundary value problem for a mixed functionally differential advancing-lagging equation with fractional derivative ⋮ Optical buffering in stationary structures

Cites Work

• Numerical optimization of the two-dimensional transformation of arguments in the functional-differential diffusion equation
• Travelling wave dynamics in a nonlinear interferometer with spatial field transformer in feedback
• Bifurcation of periodic solutions for nonlinear parabolic functional differential equations arising in optoelectronics
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