Publicação
An evolutionary vector-valued variational inequality and Lagrange multiplier
| Resumo: | We prove existence and uniqueness of solution of an evolutionary vector-valued variational inequality de ned in the convex set of vector valued functions v subject to the constraint |v| ≤ 1. We show that we can write the variational inequality as a system of equations on the unknowns (λ,u), where λ is a (unique) Lagrange multiplier belonging to L p and u solves the variational inequality. Given data (f n,un0) converging to (f,u0) in L ∞(QT ) × H1 0 (Ω), we prove the convergence of the solutions (λn,un) of the Lagrange multiplier problem to the solution of the limit problem, when we let n → ∞. |
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| Autores principais: | Azevedo, Davide Manuel Santos |
| Outros Autores: | Santos, Lisa |
| Assunto: | Continuous dependence Evolutionary vector-valued variational inequalities Lagrange multipliers |
| Ano: | 2025 |
| País: | Portugal |
| Tipo de documento: | artigo |
| Tipo de acesso: | acesso aberto |
| Instituição associada: | Universidade do Minho |
| Idioma: | inglês |
| Origem: | RepositóriUM - Universidade do Minho |
| Resumo: | We prove existence and uniqueness of solution of an evolutionary vector-valued variational inequality de ned in the convex set of vector valued functions v subject to the constraint |v| ≤ 1. We show that we can write the variational inequality as a system of equations on the unknowns (λ,u), where λ is a (unique) Lagrange multiplier belonging to L p and u solves the variational inequality. Given data (f n,un0) converging to (f,u0) in L ∞(QT ) × H1 0 (Ω), we prove the convergence of the solutions (λn,un) of the Lagrange multiplier problem to the solution of the limit problem, when we let n → ∞. |
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