Results 1 to 10 of about 24,624 (181)
Regularity of Time-Periodic Solutions to Autonomous Semilinear Hyperbolic PDEs [PDF]
Journal of Mathematical Analysis and Applications, 2023 This paper concerns autonomous boundary value problems for 1D semilinear hyperbolic PDEs. For time-periodic classical solutions, which satisfy a certain non-resonance condition, we show the following: If the PDEs are continuous with respect to the space variable $x$ and $C^\infty$-smooth with respect to the unknown function $u$, then the solution is $C^
Irina Kmit, Lutz Recke
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Computer assisted proof of branches of stationary and periodic solutions, and Hopf bifurcations, for dissipative PDEs [PDF]
Communications in Nonlinear Science and Numerical Simulation, 2021 We discuss an approach to the computer assisted proof of the existence of branches of stationary and periodic solutions for dissipative PDEs, using the Brussellator system with diffusion and Dirichlet boundary conditions as an example, We also consider the case where the branch of periodic solutions emanates from a branch of stationary solutions ...
Gianni Arioli
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Time-periodic solutions of Hamiltonian PDEs using pseudoholomorphic curves [PDF]
Algebraic & Geometric Topology, 2023 We extend the pseudoholomorphic curve methods from Floer theory to infinite-dimensional phase spaces and use our results to prove the existence of a forced time-periodic solution to a general Hamiltonian PDE with regularizing nonlinearity. In particular, when the nonlinearity is sufficiently regularizing, bounded and time-periodic, we prove an infinite-
Oliver Fabert, Niek Lamoree
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Families of Periodic Solutions for Some Hamiltonian PDEs [PDF]
SIAM Journal on Applied Dynamical Systems, 2017 This work studies time-periodic solutions for two Hamiltonian PDE's on a finite interval \([0,\pi]\): the nonlinear wave equation \(u_{tt}-u_{xx}=\pm u^3\), with Dirichlet boundary conditions, and the nonlinear beam equation \(u_{tt}+u_{xxxx}=\pm u^3\) on a finite interval with Navier boundary conditions (the function and its second derivative vanishes
Gianni Arioli, Hans Koch
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Quasi-periodic solutions of Hamiltonian PDEs [PDF]
Journées équations aux dérivées partielles, 2012 We overview recent existence results and techniques about KAM theory for PDEs.
Massimiliano Berti
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Rigorous numerics for PDEs with indefinite tail: existence of a periodic solution of the Boussinesq equation with time-dependent forcing [PDF]
, 2015 We consider the Boussinesq PDE perturbed by a time-dependent forcing. Even though there is no smoothing effect for arbitrary smooth initial data, we are able to apply the method of self-consistent bounds to deduce the existence of smooth classical ...
Aleksander Czechowski +1 more
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Communications in Nonlinear Science and Numerical Simulation, 2020 In this paper we study the continuous and full discrete versions of a parabolic-parabolic-elliptic system with periodic terms that serves as a model for some chemotaxis phenomena. This model appears naturally in the interaction of two biological species and a chemical.
Mihaela Negreanu, A.M. Vargas
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Quasi-periodic solutions of PDEs [PDF]
Séminaire Laurent Schwartz — EDP et applications, 2014 The aim of this talk is to present some recent existence results about quasi-periodic solutions for PDEs like nonlinear wave and Schrödinger equations in 𝕋 d , d≥2, and the 1-d derivative wave equation. The proofs are based on both Nash-Moser implicit function theorems and KAM theory.
Massimiliano Berti
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Approximation of periodic PDE solutions with anisotropic translation invariant spaces [PDF]
2017 International Conference on Sampling Theory and Applications (SampTA), 2017 We approximate the quasi-static equation of linear elasticity in translation invariant spaces on the torus. This unifies different FFT-based discretisation methods into a common framework and extends them to anisotropic lattices. We analyse the connection between the discrete solution spaces and demonstrate the numerical benefits.
Ronny Bergmann, Dennis Merkert
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Periodic Solutions and Asymptotic Behavior of a PDE with Hysteresis in the Source Term [PDF]
Rocky Mountain Journal of Mathematics, 2006 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jana Kopfová
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