5,411 research outputs found
Mixed problems for degenerate abstract parabolic equations and applications
Degenerate abstract parabolic equations with variable coefficients are
studied. Here the boundary conditions are nonlocal. The maximal regularity
properties of solutions for elliptic and parabolic problems and Strichartz type
estimates in mixed spaces are obtained. Moreover, the existence and
uniqueness of optimal regular solution of mixed problem for nonlinear parabolic
equation is established. Note that, these problems arise in fluid mechanics and
environmental engineering
The Cauchy problem for operator-Boussinesq equations
In this paper, the existence and uniqueness of solution of the Cauchy problem
for abstract Boussinesq equation is obtained. By applying this result, the
Cauchy problem for systems of Boussinesq equations of finite or infinite orders
are studie
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