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math.AP2024★ 5 cited
A rigorous integrator and global existence for higher-dimensional semilinear parabolic PDEs via semigroup theory
Gabriel William Duchesne, Jean-Philippe Lessard, Akitoshi Takayasu
In this paper, we introduce a general constructive method to compute solutions of initial value problems of semilinear parabolic partial differential equations on hyper-rectangular…
math.AP2020
Global dynamics in nonconservative nonlinear Schrödinger equations
Jonathan Jaquette, Jean-Philippe Lessard, Akitoshi Takayasu
In this paper, we study the global dynamics of a class of nonlinear Schrödinger equations using perturbative and non-perturbative methods. We prove the semi-global existence of sol…