Abstract elliptic operators appearing in atmospheric dispersion

作者：Shakhmurov Veli B^*; Sahmurova Aida

来源：Boundary Value Problems, 2014, 2014(1): 43.

DOI：10.1186/1687-2770-2014-43

• separable boundary value problems
• equations with variable coefficients
• estimates of the resolvent
• differential-operator equations
• well-posedness for parabolic problems
• reaction-diffusion equations

In this paper, the boundary value problem for the differential-operator equation with principal variable coefficients is studied. Several conditions for the separability and regularity in abstract L-p-spaces are given. Moreover, sharp uniform estimates for the resolvent of the corresponding elliptic differential operator are shown. It is implies that this operator is positive and also is a generator of an analytic semigroup. Then the existence and uniqueness of maximal regular solution to nonlinear abstract parabolic problem is derived. In an application, maximal regularity properties of the abstract parabolic equation with variable coefficients and systems of parabolic equations are derived in mixed L-p-spaces.

• 出版日期2014-2-19