On Hyperbolic Initial-Boundary Value Problems with a Strictly Dissipative Boundary Condition

2020 ◽  
pp. 125-144
Author(s):  
Matthias Eller
Keyword(s):  
Boundary Condition ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problems ◽  
Dissipative Boundary ◽  
Initial Boundary Value ◽  
Dissipative Boundary Condition

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

2013 ◽  
Vol 2013 ◽  
pp. 1-20 ◽  
Author(s):  
Mykola Krasnoschok ◽  
Nataliya Vasylyeva
Keyword(s):  
Boundary Condition ◽  
Boundary Value Problems ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Initial Boundary ◽  
Dynamic Boundary Condition ◽  
Initial Boundary Value Problems ◽  
Dynamic Boundary ◽  
Contraction Theorem ◽  
Initial Boundary Value

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

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