A5080179247- Nonlinear Partial Differential Equations
- Stability and Controllability of Differential Equations
- Advanced Mathematical Modeling in Engineering
- Advanced Mathematical Physics Problems
- Nonlinear Differential Equations Analysis
- Differential Equations and Boundary Problems
- Numerical methods in inverse problems
- advanced mathematical theories
- Fractional Differential Equations Solutions
- Differential Equations and Numerical Methods
- Navier-Stokes equation solutions
- Mathematical Biology Tumor Growth
- Advanced Harmonic Analysis Research
- Geometric Analysis and Curvature Flows
- Phytochemicals and Antioxidant Activities
- Topology Optimization in Engineering
- Soviet and Russian History
- Algebraic and Geometric Analysis
- Cellular Mechanics and Interactions
- Energy and Environmental Systems
- Composite Structure Analysis and Optimization
- Structural Analysis and Optimization
- Plant Physiology and Cultivation Studies
- Advanced Chemical Physics Studies
- Gene Regulatory Network Analysis
Saga University
2018-2025
Ryukoku University
2018-2024
Shimane University
2021
Osaka Prefecture University
2013-2017
Tohoku University
2008-2017
Hiroshima University
2011
We studythe existence and the large time behavior of global-in-time solutions a nonlinear integral equation with generalized heat kernel\begin{eqnarray*} & u(x,t)=\int_{{\mathbb R}^N}G(x-y,t)\varphi(y)dy\\ \qquad\quad+\int_0^t\int_{{\mathbb R}^N}G(x-y,t-s)F(y,s,u(y,s),\dots,\nabla^\ell u(y,s))dyds,\end{eqnarray*}where $\varphi\in W^{\ell,\infty}({\mathbb R}^N)$ $\ell\in\{0,1,\dots\}$.The arguments this paper are applicable tothe Cauchy problem for various parabolic equationssuch as...
We study the large time behavior of solutions for Cauchy problem, ∂ t u = Δu + a(x, t)u in ℝ N × (0, ∞), (x, 0) Q(x) , where Q ∈ L 1 (ℝ (1+|x| K ) dx) with ≥ 0 and ∥a(t)∥ ∞ O(t -A as → some A > 1. In this paper we classify decay rate give precise estimates on difference between their asymptotic profiles. Furthermore, an application, discuss global semilinear heat equation, λ|u| p-1 u, λ p
We study the large time behavior of positive solutions forthe Laplace equation on half-space with a nonlinear dynamical boundary condition.We show convergence to Poisson kernel in suitable sense provided initial dataare sufficiently small.
We consider the Cauchy problem for a nonlinear damped wave equation. Under suitable assumptions of term and initial functions, has global-in-time solution $u$ behaving like Gauss kernel as time tends to infinity. In this paper we show asymptotic profiles solutions give precise decay estimates on difference between their profiles. Our results are based $L^p$--$L^q$-type decomposition fundamental linearized equation expansion heat
The main purpose of the paper is to study large-time behavior positive solutions a semilinear elliptic equation with dynamical boundary condition. We show that small behave asymptotically like suitable multiples Poisson kernel.
We consider the Cauchy problem of semilinear heat equation,$\partial_t u = \Delta +f(u)$ in $R^N \times (0,\infty),$$u (x,0) \phi (x) \ge 0$ $R^N,\quad\quad$where $N \geq 1$, $f \in C^1([0,\infty))$,and $\phi L^1(R^N) \cap L^{\infty}(R^N)$.We study asymptoticbehavior solutions $L^q$ spaces with $q [1,\infty]$,by using relative entropy methods.
In this paper we obtain the precise description of asymptotic behavior solution $u$ $$ \partial_t u+(-\Delta)^{\frac{\theta}{2}}u=0\quad\mbox{in}\quad{\bf R}^N\times(0,\infty), \qquad u(x,0)=\varphi(x)\quad\mbox{in}\quad{\bf R}^N, where $0<\theta<2$ and $\varphi\in L_K:=L^1({\bf R}^N,\,(1+|x|)^K\,dx)$ with $K\ge 0$. Furthermore, develop arguments in [15] [18] establish a method to expansions solutions nonlinear fractional diffusion equation...