24 citations · 53 across the 17 of their papers we have counts for
6 papers · 1 filter
Blow-up for time-fractional diffusion equations with superlinear convex semilinear terms
Xinchi Huang, Yikan Liu, Masahiro Yamamoto
This article is concerned with a semilinear time-fractional diffusion equation with a superlinear convex semilinear term in a bounded domain with the homogeneous Dirichlet, Neu…
Long-time asymptotic estimate and a related inverse source problem for time-fractional wave equations
Xinchi Huang, Yikan Liu
Lying between traditional parabolic and hyperbolic equations, time-fractional wave equations of order in time inherit both decaying and oscillating properties. In this…
Initial-boundary value problems for coupled systems of time-fractional diffusion equations
Zhiyuan Li, Xinchi Huang, Yikan Liu
This article deals with the initial-boundary value problem for a moderately coupled system of time-fractional diffusion equations. Defining the mild solution, we establish fundamen…
Well-posedness of initial-boundary value problem for time-fractional diffusion-wave equation with time-dependent coefficients
Xinchi Huang, Masahiro Yamamoto
We consider the well-posedness of the initial-boundary value problem for a time-fractional partial differential equation with the fractional order lying in (1,2]. For the case of t…
Carleman estimates for a magnetohydrodynamics system and application to inverse source problems
Xinchi Huang, Masahiro Yamamoto
In this article, we consider a linearized magnetohydrodynamics system for incompressible flow in a three-dimensional bounded domain. We first prove two kinds of Carleman estimates.…
Carleman estimates for the time-fractional advection-diffusion equations and applications
Zhiyuan Li, Xinchi Huang, Masahiro Yamamoto
In this article, we prove Carleman estimates for the generalized time-fractional advection-diffusion equations by considering the fractional derivative as perturbation for the firs…