Well-posedness of fractional parabolic equations
β Scribed by Allaberen Ashyralyev
- Book ID
- 120736061
- Publisher
- Springer International Publishing AG
- Year
- 2013
- Tongue
- English
- Weight
- 251 KB
- Volume
- 2013
- Category
- Article
- ISSN
- 1687-2762
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π SIMILAR VOLUMES
## Abstract We study the (__W__^Ξ±, __p__^, __L__^__p__^)βmild wellβposedness of the equation with fractional derivative __D__^Ξ±^__u__(__t__) = __Au__(__t__) + __f__(__t__),β0 β€ __t__ β€ 2Ο, where __A__ is a closed operator in a Banach space __X__, Ξ± > 0,β1 β€ __p__ < β and __D__^Ξ±^ is the fractional
We develop a well-posedness theory for solutions in L 1 to the Cauchy problem of general degenerate parabolic-hyperbolic equations with non-isotropic nonlinearity. A new notion of entropy and kinetic solutions and a corresponding kinetic formulation are developed which extends the hyperbolic case. T