Existence and Uniqueness of the Solutions for Some Initial-Boundary Value Problems with the Fractional Dynamic Boundary Condition | Zendy

Mykola Krasnoschok | Zendy; Nataliya Vasylyeva | Zendy

Open Access

Existence and Uniqueness of the Solutions for Some Initial-Boundary Value Problems with the Fractional Dynamic Boundary Condition

Author(s) -

Mykola Krasnoschok,

Nataliya Vasylyeva

Publication year - 2013

Publication title -

international journal of partial differential equations

Language(s) - English

Resource type - Journals

eISSN - 2356-7082

pISSN - 2314-6524

DOI - 10.1155/2013/796430

Subject(s) - uniqueness , mathematics , boundary value problem , mathematical analysis , bounded function , contraction mapping , mixed boundary condition , domain (mathematical analysis) , nonlinear system , operator (biology) , poincaré–steklov operator , boundary (topology) , robin boundary condition , fixed point theorem , physics , biochemistry , chemistry , repressor , quantum mechanics , gene , transcription factor

In this paper, we analyze some initial-boundary value problems forthe subdiffusion equation with a fractional dynamic boundary condition in aone-dimensional bounded domain. First, we establish the unique solvabilityin the Hölder space of the initial-boundary value problems for the equation , , where L is a uniformly ellipticoperator with smooth coefficients with the fractional dynamic boundary condition. Second, we apply the contraction theorem to prove the existence anduniqueness locally in time in the Hölder classes of the solution to the corresponding nonlinear problems

The content you want is available to Zendy users.

Already have an account? Click here to sign in.

Having issues? You can contact us here

Accelerating Research