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.

scholarly journals TWO INITIAL-BOUNDARY VALUE PROBLEMS WITH NONLINEAL BOUNDARY CONDITIONS FOR ONE-DIMENSION HYPERBOLIC EQUATION

2017 ◽  
Vol 17 (2) ◽  
pp. 46-56
Author(s):  
L.S. Pulkina ◽  
M.V. Strigun
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Existence And Uniqueness ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Initial Boundary ◽  
Nonlinear Boundary Conditions ◽  
One Dimension ◽  
Initial Boundary Value Problems ◽  
Initial Boundary Value

In this paper, the initial-boundary value problems for hyperbolic equationwith nonlinear boundary conditions are considered. Existence and uniqueness ofgeneralized solution are proved.

On the Existence and Uniqueness of Solutions of the Equation

1975 ◽  
Vol 18 (2) ◽  
pp. 181-187 ◽  
Author(s):  
John C. Cleménts
Keyword(s):  
Boundary Value Problems ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Quasilinear Equation ◽  
Global Solutions ◽  
Initial Boundary ◽  
Initial Boundary Value Problems ◽  
Uniqueness Of Solutions ◽  
Initial Boundary Value

AbstractThe existence and uniqueness of strong global solutions of initial-boundary value problems for the quasilinear equation utt—∂σi(uxi)/∂xi—ΔNut= f is established for functions σi(ξ), i = 1, …, N, satisfying: σi,(ξ) ∊ C1(-∞, ∞), σi(0) = 0 and for some constant K0.

scholarly journals Initial Boundary Value Problems of Semi-Linear Sub-Diffusion with Gradient Terms

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1665
Author(s):  
Yabing Gao ◽  
Yongxiang Li
Keyword(s):  
Boundary Value Problems ◽  
Operator Theory ◽  
Existence And Uniqueness ◽  
Nonlinear Term ◽  
Boundary Value ◽  
Fractional Power ◽  
Initial Boundary ◽  
Classical Solutions ◽  
Initial Boundary Value Problems ◽  
Initial Boundary Value

We consider the existence and uniqueness of the saturated classical solutions and the positive classical solutions to initial boundary value problems of semi-linear sub-diffusion with gradient terms. Applying this to the fractional power of the sectorial operator theory and the imbedding theory in the interpolation spaces, where the nonlinear term satisfies more general conditions, we obtain the existence and uniqueness of the saturated classical solutions. The results obtained generalize the recent conclusions on this topic. Finally, an example is given to illustrate the feasibility of our main results.

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