A LIOUVILLE THEOREM FOR VECTOR VALUED SEMILINEAR HEAT EQUATIONS WITH NO GRADIENT STRUCTURE AND APPLICATIONS TO BLOW-UP

作者：Nouaili Neila^*; Zaag Hatem

来源：Transactions of the American Mathematical Society, 2010, 362(7): 3391-3434.

DOI：10.1090/S0002-9947-10-04902-0

• Blow-up
• Liouville theorem
• uniform estimates
• heat equation
• vector valued

We prove a Liouville theorem for a vector valued semilinear heat equation with no gradient structure. Classical tools such as the maximum principle or energy techniques break down and have to be replaced by a new approach. We then derive from tins theorem uniform estimates for blow-up solutions of that equation.

• 出版日期2010-7