## Abstract We are concerned with the problem of determining the sharp regularity of the coefficients with respect to the time variable __t__ in order to have a wellβposed Cauchy problem in __H__^β^ or in Gevrey classes for linear or quasilinear hyperbolic operators of higher order. We use and mix
Parabolic equations with unbounded coefficients
β Scribed by D.G Aronson; P Besala
- Publisher
- Elsevier Science
- Year
- 1967
- Tongue
- English
- Weight
- 594 KB
- Volume
- 3
- Category
- Article
- ISSN
- 0022-0396
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
## Abstract The Cauchy problem for nonlinear parabolic differentialβfunctional equations is considered. Under natural generalized Lipschitzβtype conditions with weights, the existence and uniqueness of unbounded solutions is obtained in three main cases: (i) the functional dependence __u__(__Β·__);
A general Hilbert-space-based stochastic averaging theory is brought forth herein for arbitrary-order parabolic equations with (possibly long range dependent) random coefficients. We use regularity conditions on t u = (t, x)= : which are slightly stronger than those required to prove pathwise exist