solidot新版网站常见问题,请点击这里查看。
消息
本文已被查看5167次
Deterministic and Stochastic Cauchy problems for a class of weakly hyperbolic operators on R^n. (arXiv:1810.05009v1 [math.AP])
来源于:arXiv
We study a class of hyperbolic Cauchy problems, associated with linear
operators and systems with polynomially bounded coefficients, variable
multiplicities and involutive characteristics, globally defined on R^n. We
prove well-posedness in Sobolev-Kato spaces, with loss of smoothness and decay
at infinity. We also obtain results about propagation of singularities, in
terms of wave-front sets describing the evolution of both smoothness and decay
singularities of temperate distributions. Moreover, we can prove the existence
of random-field solutions for the associated stochastic Cauchy problems. To
this aim, we first discuss algebraic properties for iterated integrals of
suitable parameter-dependent families of Fourier integral operators, associated
with the characteristic roots, which are involved in the construction of the
fundamental solution. In particular, we show that, also for this operator
class, the involutiveness of the characteristics implies commutative properties
for such e 查看全文>>