A5070131704- Advanced Mathematical Modeling in Engineering
- Nonlinear Partial Differential Equations
- Stability and Controllability of Differential Equations
- Nonlinear Differential Equations Analysis
- Advanced Mathematical Physics Problems
- Differential Equations and Numerical Methods
- Contact Mechanics and Variational Inequalities
- Numerical methods in inverse problems
- Fractional Differential Equations Solutions
- Nonlinear Dynamics and Pattern Formation
- Advanced Numerical Methods in Computational Mathematics
- Navier-Stokes equation solutions
- Fluid Dynamics and Turbulent Flows
- Solidification and crystal growth phenomena
- Mathematical Biology Tumor Growth
- Composite Material Mechanics
- Numerical methods in engineering
- Optimization and Variational Analysis
- Mathematical and Theoretical Analysis
- Advanced Differential Geometry Research
- Geometric Analysis and Curvature Flows
- Service-Oriented Architecture and Web Services
- Stochastic processes and statistical mechanics
- 3D Modeling in Geospatial Applications
- Advanced Computational Techniques and Applications
Tohoku University
2015-2024
University of Graz
2023
Mathematical Institute of the Slovak Academy of Sciences
2023
Technical University of Munich
2015-2018
Helmholtz Zentrum München
2016-2018
Kobe University
2012-2016
Shibaura Institute of Technology
2007-2011
Waseda University
2004-2007
Nihon University
2007
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 time existence (continuous) strong solutions evolution equations governed by the difference two subdifferential operators To prove these results, fractional chain-rule formulae, a Lipschitz perturbation convex Gronwall-type lemmas nonlinear Volterra integral inequalities are developed. They also play crucial...
We present a variational reformulation of class doubly nonlinear parabolic equations as (limits of) constrained convex minimization problems. In particular, an $\varepsilon$-dependent family weighted energy-dissipation (WED) functionals on entire trajectories is introduced and proved to admit minimizers. These minimizers converge solutions the original equation $\varepsilon \to 0$. The argument relies suitable dualization former analysis [G. Akagi U. Stefanelli, J. Funct. Anal., 260 (2011),...
Abstract This paper is concerned with a quantitative analysis of asymptotic behaviors (possibly sign-changing) solutions to the Cauchy–Dirichlet problem for fast diffusion equation posed on bounded domains Sobolev subcritical exponents. More precisely, rates convergence non-degenerate profiles are revealed via an energy method. The sharp rate positive ones was recently discussed by Bonforte and Figalli (Commun Pure Appl Math 74:744-789, 2021) based entropy An alternative proof their result...
.This paper deals with a receptor-based model which arises from the modeling of interactions between intracellular processes and diffusible signaling factors. We prove existence stationary solutions jump discontinuity by variational method. Then singular perturbation problem discontinuous nonlinearity is studied based on patching argument implicit function theorem, to obtain solution single transition layer. Moreover, we derive sufficient condition for stability discontinuity. In addition,...
Abstract Let H be a norm of <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msup> <m:mi>ℝ</m:mi> <m:mi>N</m:mi> </m:msup> </m:math> {\mathbb{R}^{N}} and <m:msub> <m:mi>H</m:mi> <m:mn>0</m:mn> </m:msub> {H_{0}} the dual . Denote by <m:mi mathvariant="normal">Δ</m:mi> {\Delta_{H}} Finsler–Laplace operator defined <m:mrow> <m:mo></m:mo> <m:mi>u</m:mi> </m:mrow> <m:mo>:=</m:mo> <m:mi>div</m:mi> <m:mo></m:mo> <m:mo stretchy="false">(</m:mo> <m:mo>∇</m:mo> stretchy="false">)</m:mo>...