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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 $0hat there are three kinds of blowup solutions in this equation. I... 
DIFFERENTIAL HARNACK ESTIMATES FOR BACKWARD HEAT EQUATIONS WITH POTENTIALS UNDER THE RICCI FLOW
HARNACK ESTIMATES WITH POTENTIALS UNDER THE RICCI FLOW
2015/8/17
In this paper, we derive a general evolution formula for possible Harnack quantities. As a consequence, we prove several differential Harnack inequalities
for positive solutions of backward hea...
A Gaussian estimate for the Heat Kernel on differential forms and application to the Riesz transform
Gaussian the Heat Kernel differential forms
2010/11/24
Let $(M^m,g)$ be a m-dimensional complete Riemannian manifold which satisfies the n-Sobolev inequality and on which the volume growth is comparable to the one of $\R^n$ for big balls; if the Hodge Lap...
Symmetry analysis and exact solutions of semilinear heat flow in multi-dimensions
Symmetry analysis exact solutions semilinear heat flow in multi-dimensions
2010/11/24
A symmetry group method is used to obtain exact solutions for a semilinear radial heat equation in $n>1$ dimensions with a general power nonlinearity. The method involves an ansatz technique to solve...
A nonlocal quasilinear multi-phase system with nonconstant specific heat and heat conductivity
A nonlocal quasilinear multi-phase system nonconstant specific heat heat conductivity
2010/11/23
In this paper, we prove the existence and global boundedness from above for a solution to an integrodifferential model for nonisothermal multi-phase transitions under nonhomogeneous third type bounda...
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...
Heat conduction: a telegraph-type model with self-similar behavior of solutions II
Heat conduction telegraph-type model self-similar behavior of solutions II
2010/12/15
In our former study (J. Phys. A: Math. Theor. 43, (2010) 325210 or arXiv:1002.0999v1 [math-
ph]) we introduced a modified Fourier-Cattaneo law and derived a non-autonomous telegraph-type
heat conduc...