Data di Pubblicazione:
2010
Citazione:
Abstract parabolic equations with applications to problems in cylindrical space domains / M. Di Cristo, D. Guidetti, A. Lorenzi. - In: ADVANCES IN DIFFERENTIAL EQUATIONS. - ISSN 1079-9389. - 15:1-2(2010), pp. 1-42.
Abstract:
In a Banach space $X$ we consider the partial differential equation $$
(*)\quad D_{t}u(t,x)+(-1)^ma(x)D_{x}^{2m}u(t,x)-A(x)u(t,x)=f(t,x)$$, where $m$ is a positive integer, related to the rectangle $(0,T)\times(0,L)$ and the family of closed linear operators $\{A(x)\}_{x\in[0,L]}$.
Under suitable assumptions we uniquely solve the initial and boundary value problem associated with $(*)$. Some applications are given when $A(x)$ are explicit linear uniformly elliptic differential operators.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Abstract partial differential and boundary
value problems. Existence and uniqueness results. Parabolic and ultraparabolic boundary value problem in cylindrical domains.
Elenco autori:
M. Di Cristo, D. Guidetti, A. Lorenzi
Link alla scheda completa: