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The direct and inverse problem for sub-diffusion equations with a generalized impedance subregion

Isaac Harris (2022)

Applications of Mathematics

In this paper, we consider the direct and inverse problem for time-fractional diffusion in a domain with an impenetrable subregion. Here we assume that on the boundary of the subregion the solution satisfies a generalized impedance boundary condition. This boundary condition is given by a second order spatial differential operator imposed on the boundary. A generalized impedance boundary condition can be used to model corrosion and delimitation. The well-posedness for the direct problem is established...

The Dirichlet problem for elliptic equations in the plane

Paola Cavaliere, Maria Transirico (2005)

Commentationes Mathematicae Universitatis Carolinae

In this paper an existence and uniqueness theorem for the Dirichlet problem in W 2 , p for second order linear elliptic equations in the plane is proved. The leading coefficients are assumed here to be of class VMO.

The dyadic fractional diffusion kernel as a central limit

Hugo Aimar, Ivana Gómez, Federico Morana (2019)

Czechoslovak Mathematical Journal

We obtain the fundamental solution kernel of dyadic diffusions in ℝ + as a central limit of dyadic mollification of iterations of stable Markov kernels. The main tool is provided by the substitution of classical Fourier analysis by Haar wavelet analysis.

The existence of Carathéodory solutions of hyperbolic functional differential equations

Adrian Karpowicz (2010)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

We consider the following Darboux problem for the functional differential equation ∂ ² u / ∂ x ∂ y ( x , y ) = f ( x , y , u ( x , y ) , ∂ u / ∂ x ( x , y ) , ∂ u / ∂ y ( x , y ) ) a.e. in [0,a]×[0,b], u(x,y) = ψ(x,y) on [-a₀,a]×[-b₀,b] 0 , a ] × ( 0 , b ] , where the function u ( x , y ) : [ - a ₀ , 0 ] × [ - b ₀ , 0 ] → ℝ k is defined by u ( x , y ) ( s , t ) = u ( s + x , t + y ) for (s,t) ∈ [-a₀,0]×[-b₀,0]. We prove a theorem on existence of the Carathéodory solutions of the above problem.

Currently displaying 21 – 40 of 110