A phase field approach for optimal boundary control of damage processes in two-dimensional viscoelastic media

DOI10.1142/S0218202515500608zbMath1325.35212arXiv1502.02952MaRDI QIDQ3451157

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Publication date: 10 November 2015

Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1502.02952

zbMATH Keywords

optimal controlphase field modelwell-posednessviscoelasticitydamage processesnonlinear parabolic inclusions

Mathematics Subject Classification ID

Brittle fracture (74R10) Theories of fracture and damage (74A45) Nonlinear constitutive equations for materials with memory (74D10) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Optimization problems in solid mechanics (74P99) Existence theories for optimal control problems involving partial differential equations (49J20) Existence of solutions of dynamical problems in solid mechanics (74H20) Uniqueness of solutions of dynamical problems in solid mechanics (74H25) PDEs in connection with mechanics of deformable solids (35Q74) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Strong solutions to PDEs (35D35) Initial-boundary value problems for mixed-type systems of PDEs (35M33) Unilateral problems for mixed-type systems of PDEs and systems of variational inequalities with partial differential operators of mixed type (35M87)

Related Items (10)

A polynomial-augmented RBF collocation method using fictitious centres for solving the Cahn-Hilliard equation ⋮ Existence of solution to a Cahn–Hilliard equation ⋮ Necessary conditions of first-order for an optimal boundary control problem for viscous damage processes in 2D ⋮ Second-order optimality conditions for an optimal control problem governed by a regularized phase-field fracture propagation model ⋮ A benchmark problem for the two- and three-dimensional Cahn-Hilliard equations ⋮ Basic principles and practical applications of the Cahn-Hilliard equation ⋮ An efficient second-order energy stable BDF scheme for the space fractional Cahn-Hilliard equation ⋮ Shape Optimization for a Class of Semilinear Variational Inequalities with Applications to Damage Models ⋮ An Optimal Control Problem Governed by a Regularized Phase-Field Fracture Propagation Model. Part II: The Regularization Limit ⋮ Doubly nonlocal Cahn-Hilliard equations. Well-posedness and asymptotic behavior

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