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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Type II blowup solutions to the 5D semilinear heat equation with double power nonlinearity
双幂非线性 5D 双线性热方程 II型爆破解
2023/5/16
We will discuss the existence of blowup solutions to $u_t=\Delta u+|u|^\frac{4}{n-2}u-|u|^{q-1}u$ with $0e show that there are three kinds of blowup solutions in this equation. I... 
THE CONJUGATE HEAT EQUATION AND ANCIENT SOLUTIONS OF THE RICCI FLOW
ANCIENT SOLUTIONS CONJUGATE HEAT EQUATION
2015/8/17
We prove Gaussian type bounds for the fundamental solution of the conjugate heat equation evolving under the Ricci flow. As a consequence, for dimension 4 and
higher, we show that the backward ...
The paper considers a manifold M evolving under the Ricci
ow and establishes a series of gradient
estimates for positive solutions of the heat equation on M. Among other results, we prove Li-Yau-ty...
On the (strict) positivity of solutions of the stochastic heat equation
the stochastic heat equation Probability
2012/6/30
We give a new proof of the fact that the solutions of the stochastic heat equation, started with non-negative initial conditions, are strictly positive at positive times. The proof uses concentration ...
Asymptotic behavior for the heat equation in nonhomogeneous media with critical density
heat equation non-homogeneous media singular density asymptotic behavior radially symmetric solutions
2012/6/21
We study the asymptotic behavior of solutions to the heat equation in nonhomogeneous media with critical singular density $$ |x|^{-2}\partial_{t}u=\Delta u, \quad \hbox{in} \ \real^N\times(0,\infty). ...
Heat equation for weighted Banach space valued function spaces
Laplace operator holomorphic semigroups weighted Banach space valued function spaces Functional Analysis
2012/6/21
We study the homogeneous equation (*) $ u' = \Delta u$, $t > 0$, $u(0)=f\in wX$, where $wX$ is a weighted Banach space, $w(x)= (1+||x||)^k$, $x\in \r^n$ with $k\ge 0$, $ \Delta$ is the Laplacian, $Y$ ...
It is known that a bounded solution of the heat equation in a half-space which becomes zero at some time must be identically zero, even though no assumptions are made on the boundary values of the so...
Gradient estimates for a simple nonlinear heat equation on manifolds
nonlinear heat equation gradient estimate
2010/11/29
In this paper, we study the gradient estimate for positive solutions to the following nonlinear heat equation problem ut − u = au log u + V u, u > 0 on the compact Riemannian manifold (M, g) of...
Approximate analytical solution of 3D fractional microscale heat equation using modified homotopy perturbation method
Homotopy Perturbation Method (HPM) Three-dimensional heat transport equation heat flux gradient
2010/9/14
In the present article, we use modified homotopy perturbation method (HPM) to find approximate analytical solution of three-dimensional time fractional microscale heat transport equation. This transpo...
Fourth-order method for non-homogeneous heat equation with nonlocal boundary conditions
Heat equation non-local boundary conditions fourth-order numerical methods
2010/9/15
In this paper a fourth-order numerical scheme is developed and implemented for the solution of non-homogeneous heat equation ut = uxx + q(x, t) with integral boundary conditions. The results obtained ...
The Stochastic Heat Equation with Fractional-Colored Noise:Existence of the Solution
Stochastic heat equation Gaussian noise stochastic integral fractional Brownian motion spatial covariance function
2009/6/12
The Stochastic Heat Equation with Fractional-Colored Noise:Existence of the Solution.
Application of the Adomian decomposition method for solving the heat equation in the cast-mould heterogeneous domain
Application of information technology to the foundry industry Heat conduction Adomian decomposition method
2011/4/1
The paper is focused on a method for solving the heat equation in a cast-mould heterogeneous domain. The discussed method makes use of the Adomian decomposition method. The derived calculations prove ...
A connection between the stochastic heat equation and fractional Brownian motion, and a simple proof of a result of Talagrand
heat equation white noise stochastic partial differential equations
2009/4/29
We give a new representation of fractional Brownian motion with Hurst parameter $Hleqfrac{1}{2}$ using stochastic partial differential equations. This representation allows us to use the Markov proper...
On the Duality between Coalescing Brownian Particles and the Heat Equation Driven by Fisher-Wright Noise
Coalesce duality entrance law Fisher-Wright noise particle system
2009/4/24
This paper concerns the Markov process duality between the one-dimensional heat equation driven by Fisher-Wright white noise and slowly coalescing Brownian particles. A representation is found for the...
A connection between the stochastic heat equation and fractional Brownian motion, and a simple proof of a result of Talagrand
stochastic fractional Brownian motion
2009/4/22
We give a new representation of fractional Brownian motion with Hurst parameter $Hleqfrac{1}{2}$ using stochastic partial differential equations. This representation allows us to use the Markov proper...