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Open AccessSaddle-Type Blow-Up Solutions with Computer-Assisted Proofs: Validation and Extraction of Global Nature
In this paper, blow-up solutions of autonomous ordinary differential equations (ODEs) which are unstable under perturbations of initial points, referred to as saddle-type blow-up solutions, are studied. Combining...
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Open AccessCorrection to: Rigorous numerics for nonlinear heat equations in the complex plane of time
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Open AccessRigorous numerics for nonlinear heat equations in the complex plane of time
In this paper, we introduce a method for computing rigorous local inclusions of solutions of Cauchy problems for nonlinear heat equations for complex time values. The proof is constructive and provides explici...