5,653 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
Hyers-Ulam stability for coupled random fixed point theorems and applications to periodic boundary value random problems
In this paper, we prove some existence, uniqueness and Hyers-Ulam stability results for the coupled random fixed point of a pair of contractive type random operators on separable complete metric spaces. The approach is based on a new version of the Perov type fixed point theorem for contractions. Some applications to integral equations and to boundary value problems are also given.Ministerio de Economía y Competitividad (MINECO). EspañaEuropean Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER)Junta de Andalucí
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
Regularity of Ornstein-Uhlenbeck processes driven by a L{\'e}vy white noise
The paper is concerned with spatial and time regularity of solutions to
linear stochastic evolution equation perturbed by L\'evy white noise "obtained
by subordination of a Gaussian white noise". Sufficient conditions for spatial
continuity are derived. It is also shown that solutions do not have in general
\cadlag modifications. General results are applied to equations with fractional
Laplacian. Applications to Burgers stochastic equations are considered as well.Comment: This is an updated version of the same paper. In fact, it has already
been publishe
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