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Papers by Adrian Viorel
Journal of Mathematical Analysis and Applications, 2016
Abstract In this work we investigate the existence of solutions for semilinear Cauchy problems wi... more Abstract In this work we investigate the existence of solutions for semilinear Cauchy problems with nonlocal initial conditions in the neighborhood of an asymptotically stable equilibrium point of the evolution equation. Using Granas' continuation principle for contractive maps and the qualitative theory of differential equations in Banach spaces, under mild assumptions, we prove the existence of a unique solution. We also show that the main abstract result can be applied to nonlocal initial boundary value problems for reaction–diffusion equations with non-convex nonlinearities.
arXiv (Cornell University), Oct 16, 2013
Applied Mathematics Letters, 2018
Journal of Mathematical Analysis and Applications, 2016
Abstract In this work we investigate the existence of solutions for semilinear Cauchy problems wi... more Abstract In this work we investigate the existence of solutions for semilinear Cauchy problems with nonlocal initial conditions in the neighborhood of an asymptotically stable equilibrium point of the evolution equation. Using Granas' continuation principle for contractive maps and the qualitative theory of differential equations in Banach spaces, under mild assumptions, we prove the existence of a unique solution. We also show that the main abstract result can be applied to nonlocal initial boundary value problems for reaction–diffusion equations with non-convex nonlinearities.
Studia Universitatis Babes-Bolyai Matematica, 2020
Numerical Algorithms, Jul 13, 2019
Discrete and Continuous Dynamical Systems, 2021
Journal of Optimization Theory and Applications, Jan 9, 2015
Numerical Functional Analysis and Optimization, Apr 29, 2015
Discrete and Continuous Dynamical Systems, 2021
The present work deals with the numerical long-time integration of damped Hamiltonian systems. Th... more The present work deals with the numerical long-time integration of damped Hamiltonian systems. The method that we analyze combines a specific Strang splitting, that separates linear dissipative effects from conservative ones, with an energy-preserving averaged vector field (AVF) integrator for the Hamiltonian subproblem. This construction faithfully reproduces the energy-dissipation structure of the continuous model, its equilibrium points and its natural Lyapunov function. As a consequence of these structural similarities, both the convergence to equilibrium and, more interestingly, the energy decay rate of the continuous dynamical system are recovered at a discrete level. The possibility of replacing the implicit AVF integrator by an explicit Stormer-Verlet one is also discussed, while numerical experiments illustrate and support the theoretical findings.
Numerical Algorithms, 2019
In the present work we deal with set-valued equilibrium problems for which we provide sufficient ... more In the present work we deal with set-valued equilibrium problems for which we provide sufficient conditions for the existence of a solution. The conditions that we consider are imposed not on the whole domain, but rather on a self segment-dense subset of it, a special type of dense subset. As an application, we obtain a generalized Debreu-Gale-Nikaido-type theorem, with a considerably weakened Walras law in its hypothesis. Further, we consider a non-cooperative n-person game and prove the existence of a Nash equilibrium, under assumptions that are less restrictive than the classical ones.
Numerical Functional Analysis and Optimization, 2015
Journal of Optimization Theory and Applications, 2015
Journal of Mathematical Analysis and Applications, 2016
Abstract In this work we investigate the existence of solutions for semilinear Cauchy problems wi... more Abstract In this work we investigate the existence of solutions for semilinear Cauchy problems with nonlocal initial conditions in the neighborhood of an asymptotically stable equilibrium point of the evolution equation. Using Granas' continuation principle for contractive maps and the qualitative theory of differential equations in Banach spaces, under mild assumptions, we prove the existence of a unique solution. We also show that the main abstract result can be applied to nonlocal initial boundary value problems for reaction–diffusion equations with non-convex nonlinearities.
arXiv (Cornell University), Oct 16, 2013
Applied Mathematics Letters, 2018
Journal of Mathematical Analysis and Applications, 2016
Abstract In this work we investigate the existence of solutions for semilinear Cauchy problems wi... more Abstract In this work we investigate the existence of solutions for semilinear Cauchy problems with nonlocal initial conditions in the neighborhood of an asymptotically stable equilibrium point of the evolution equation. Using Granas' continuation principle for contractive maps and the qualitative theory of differential equations in Banach spaces, under mild assumptions, we prove the existence of a unique solution. We also show that the main abstract result can be applied to nonlocal initial boundary value problems for reaction–diffusion equations with non-convex nonlinearities.
Studia Universitatis Babes-Bolyai Matematica, 2020
Numerical Algorithms, Jul 13, 2019
Discrete and Continuous Dynamical Systems, 2021
Journal of Optimization Theory and Applications, Jan 9, 2015
Numerical Functional Analysis and Optimization, Apr 29, 2015
Discrete and Continuous Dynamical Systems, 2021
The present work deals with the numerical long-time integration of damped Hamiltonian systems. Th... more The present work deals with the numerical long-time integration of damped Hamiltonian systems. The method that we analyze combines a specific Strang splitting, that separates linear dissipative effects from conservative ones, with an energy-preserving averaged vector field (AVF) integrator for the Hamiltonian subproblem. This construction faithfully reproduces the energy-dissipation structure of the continuous model, its equilibrium points and its natural Lyapunov function. As a consequence of these structural similarities, both the convergence to equilibrium and, more interestingly, the energy decay rate of the continuous dynamical system are recovered at a discrete level. The possibility of replacing the implicit AVF integrator by an explicit Stormer-Verlet one is also discussed, while numerical experiments illustrate and support the theoretical findings.
Numerical Algorithms, 2019
In the present work we deal with set-valued equilibrium problems for which we provide sufficient ... more In the present work we deal with set-valued equilibrium problems for which we provide sufficient conditions for the existence of a solution. The conditions that we consider are imposed not on the whole domain, but rather on a self segment-dense subset of it, a special type of dense subset. As an application, we obtain a generalized Debreu-Gale-Nikaido-type theorem, with a considerably weakened Walras law in its hypothesis. Further, we consider a non-cooperative n-person game and prove the existence of a Nash equilibrium, under assumptions that are less restrictive than the classical ones.
Numerical Functional Analysis and Optimization, 2015
Journal of Optimization Theory and Applications, 2015