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Yoshihito Nakajima

Publications and source records attributed to Yoshihito Nakajima.

2 recordsLinked to original sources
arXiv2026

Time-fractional nonlinear evolution equations with time-dependent constraints

This article is devoted to developing an abstract theory of time-fractional gradient flow equations for time-dependent convex functionals in real Hilbert spaces. The main results concern the existence of strong solutions to time-fractional abstract evolution equations governed by subdifferential operators of time-dependent convex functionals. In the classical theory of gradient flow equations, chain-rule formulae play a crucial role in various analyses, and such formulae for subdifferentials of time-dependent functionals are also known in the case of first-order time derivatives. In contrast, in the present setting, the presence of time-fractional derivatives prevents the direct use of the usual chain-rule. To overcome this difficulty, fractional chain-rule formulae for subdifferentials of time-dependent convex functionals are established under a nonlocal variant of the so-called Kenmochi condition. Moreover, Gronwall-type lemmas for nonlinear Volterra integral inequalities are developed. Finally, the abstract results obtained are applied to initial-boundary value problems for time-fractional degenerate parabolic equations on moving domains.

math.AP↗
arXiv2025

Time-fractional gradient flows for nonconvex energies in Hilbert spaces

This article is devoted to presenting an abstract theory on time-fractional gradient flows for nonconvex energy functionals in Hilbert spaces. Main results consist of local and global in time existence of (continuous) strong solutions to time-fractional evolution equations governed by the difference of two subdifferential operators in Hilbert spaces. To prove these results, fractional chain-rule formulae, a Lipschitz perturbation theory for convex gradient flows and Gronwall-type lemmas for nonlinear Volterra integral inequalities are developed. They also play a crucial role to cope with the lack of continuity (in time) of energies due to the subdiffusive nature of the issue. Moreover, the abstract theory is applied to the Cauchy-Dirichlet problem for some $p$-Laplace subdiffusion equations with blow-up terms complying with the so-called Sobolev (sub)critical growth condition.

math.AP↗