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Recent Posts
 [4.5.2016] Fujita blow up phenomena and hair trigger effect: the role of dispersal tails
 [3.5.2016] Global existence and Regularity results for strongly coupled nonregular parabolic systems via Iterative methods
 [29.4.2016] Dynamics near the ground state for the energy critical nonlinear heat equation in large dimensions
 [28.4.2016] Global classical solutions of the VlasovFokkerPlanck equation with local alignment forces
 [27.4.2016] Generalized entropy method for the renewal equation with measure data
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Category Archives: Entropy
Entropy method for chemical reactiondiffusion systems II: A linear system
In the last post, I’ve shown you how does the entropy method work in the case of a single equation: heat equation with homogeneous Neumann boundary condition. The application of entropy method in systems is more involved and needs more … Continue reading
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Entropy method for chemical reactiondiffusion systems I: Entropy method (continued)
In the last post, we’ve already seen the motivation of the question of convergence to equilibrium. This post continues to give a method which does not only give qualitative result (does the trajectory converge to equilibrium?) but (usually) also quantitave … Continue reading
Entropy method for chemical reactiondiffusion systems I: Entropy method
The concept “entropy method” could mean different things. In this serie of posts, I will address an entropy method which is very useful in proving convergence to equilibrium evolution equations. The main application will be in chemical reaction network theory. … Continue reading
Exponential convergence to equilibrium for a class of chemical reactions
In this post, we will see how a Lyapunov functional will help us to prove the explicit convergence to equilibrium for some chemical reactions. We consider a single reversible reaction with the forward and backward reaction rates are assumed to … Continue reading
Well posedness of a coupled PDEODE system
In this post, I simply give a proof of the well posedness of a “simple” coupled PDEODE system (which we mentioned in this post). The idea is based on “localized method”. Let is a bounded set with smooth boundary . … Continue reading
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Control the boundary value
Consider the problem (1) in an open, convex, bounded domain with the boundary condition on and intial data . We assume that . By maximum principle, we know that if is a … Continue reading
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The CsiszárKullback inequality
Today we give an inequality, which is very useful in proving the convergence of a solution to PDEs tends to the stationary solution as time tends to infinity. Lemma. Let be a domain and let satisfy and . Furthermore, let … Continue reading
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