The vanishing viscosity method for the sensitivity analysis of an optimal control problem of conservation laws in the presence of shocks

DOI10.1016/j.nonrwa.2013.02.001zbMath1292.35170OpenAlexW2042794272MaRDI QIDQ2451842

Peicheng Zhu, YaoBin Ou

Publication date: 26 May 2014

Published in: Nonlinear Analysis. Real World Applications (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/20.500.11824/526

zbMATH Keywords

matched asymptotic expansionsvariation of shock positions

Mathematics Subject Classification ID

Shocks and singularities for hyperbolic equations (35L67) First-order nonlinear hyperbolic equations (35L60) Hyperbolic conservation laws (35L65) PDEs in connection with control and optimization (35Q93)

Related Items (3)

Assessment of the effects of azimuthal mode number perturbations upon the implosion processes of fluids in cylinders ⋮ On the controllability of an advection-diffusion equation with respect to the diffusion parameter: asymptotic analysis and numerical simulations ⋮ Optimal control problem for viscous systems of conservation laws, with geometric parameter, and application to the shallow-water equations

Cites Work

• Unnamed Item
• Unnamed Item
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• Unnamed Item
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• Unnamed Item
• Nonlinear parabolic equations involving measures as initial conditions
• Generalized solutions of nonlinear parabolic equations with distributions as initial conditions
• Generalized solutions to Burgers' equation
• Viscous limits for piecewise smooth solutions to systems of conservation laws
• The linearized stability of solutions of nonlinear hyperbolic systems of conservation laws. A general numerical approach
• Dynamic solid-solid transitions with phase characterized by an order parameter
• A maximum principle for optimally controlled systems of conservation laws
• Adjoint-based derivative computations for the optimal control of discontinuous solutions of hyperbolic conservation laws
• Analytic adjoint solutions for the quasi-one-dimensional Euler equations
• AN ALTERNATING DESCENT METHOD FOR THE OPTIMAL CONTROL OF THE INVISCID BURGERS EQUATION IN THE PRESENCE OF SHOCKS
• Convergence Results for the Flux Identification in a Scalar Conservation Law
• One-dimensional transport equations with discontinuous coefficients
• Parabolic equations with conservative nonlinear term and singular initial data
• A variational calculus for discontinuous solutions of systems of conservation laws
• The partial differential equation u_t + uu_x = μ_xx

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