一类非线性伪抛物型方程Cauchy问题的适定性

Well-posedness Analysis for a Class of Nonlinear Pseudoparabolic Cauchy Problems

通过引入算子I-Δ的Bessel势将伪抛物型方程化成抽象的抛物型方程,然后利用算子半群理论讨论了一类非线性伪抛物型方程Cauchy问题的适定性问题.

This paper changes a pseudoparabolic equation into an abstract parabolic equation by introducing the Bessel potential of the operator I-Δ firstly, and then semigroup theory is applied to deal with the well-posedness of this class of nonliear pseudoparabolic Cauchy problems.