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Blowup rate estimates for the heat equation with a nonlinear gradient source term
Prof. Jong-Shenq Guo ( Tamkang University )

2008 - 10 - 23 (Thu.)
16:00 - 16:50
405, Mathematics Research Center Building (ori. New Math. Bldg.)

In this talk, we shall present some recent results on the blowup of solutions of the initial boundary value problem for the heat equation with a nonlinear gradient source term. It is shown that the blowup rate will never match that of the self-similar variables. In the one space dimensional case when assumptions are made on the initial data so that the solution is monotonically increasing in time, the exact blowup rate is found.

Time:15:30 - 16:30, Thursday, September 14, 2009 - June 30, 2010
Room:308, Mathematics Research Center Building (ori. New Math. Bldg.)
Organizer:Tai-Chia Lin ( Department of Mathematics, National Taiwan University )

Available Talk List

2008-10-02 (Thu.)		Bifurcation theory and its applications on the convection problems
2008-10-16 (Thu.)		Quantitative uniqueness for the Stokes Equations
2008-10-23 (Thu.)		Blowup rate estimates for the heat equation with a nonlinear gradient source term
2008-11-06 (Thu.)		Depth dependent stability estimate in electrical impedance tomography
2008-11-27 (Thu.)		Basic Equations of Modern Gas Dynamics
2008-12-04 (Thu.)		TBA
2008-12-18 (Thu.)		Form Strichartz Estimate to Bilinear Estimates
2008-12-31 (Wed.)		A multiscale hyperbolic system modeling cell cycles
2009-01-08 (Thu.)		From particle to kinetic and fluid descriptions on flocking
2009-01-15 (Thu.)		Stability of curved interfaces in the perturbed Allen-Cahn model
2009-01-15 (Thu.)		Diffusive synchronization of oscillations
2009-03-26 (Thu.)		An EIT problem in acoustic
2009-03-26 (Thu.)		Vacuum states for compresible Navier-Stokes equation.
2009-04-30 (Thu.)		On the symmetry properties of extremals for Hardy-Sobolev type inequalities in dimension two
2009-04-30 (Thu.)		Harnack type inequalities for singular Liouville equations
2009-06-04 (Thu.)		Combinatorics and PDEs
2009-09-24 (Thu.)		Elliptic problems on networks with constrictions
2009-10-08 (Thu.)		Spherical Averaged Endpoint Strichartz Estimates for The Two-dimensional Schrodinger Equations with Inverse Square Potential
2009-10-15 (Thu.)		Energetic variational analysis of ions in water and channels
2009-10-22 (Thu.)		Minimizers of Caffarelli-Kohn-Nirenberg inequalities with the singularity on the boundary
2009-10-29 (Thu.)		The kinetic theory approach to modeling neuronal networks
2009-11-05 (Thu.)		Instability of multi-spots in general shadow systems for reaction-diffusion equations
2009-11-12 (Thu.)		On Nonlinear Dirac Equations
2009-12-17 (Thu.)		Bilinear Strichartz estimates for Schr\"{o}dinger operators in 2 dimensional compact manifolds with boundary
2009-12-31 (Thu.)		Mathematical Analysis of the Dimensional Scaling Technique in Chemical Physics
2010-03-18 (Thu.)		Global Cauchy problem for Klein-Gordon equations with quadratic nonlinearities.
2010-03-25 (Thu.)		Large time behavior of hot spots to a linear heat equation with a potential
2010-03-25 (Thu.)		Spatial disorder of soliton solutions for discrete nonlinear Schr\"odinger equations in a $2D$ lattice
2010-04-08 (Thu.)		T-C scheme for the linear and nonlinear stability of viscous shock
2010-05-13 (Thu.)		Long-wave limit of periodic solutions of nonlinear wave equations
2010-05-13 (Thu.)		Numerical simulations of periodic initial-value problems
2010-05-20 (Thu.)		Monotonicity formulas for free boundary problems on manifolds
2010-05-20 (Thu.)		An Inverse Problem Arising in Photolithography
2010-05-27 (Thu.)		When physics meets mathematics: My personal journey