On the Operator ⨁BkRelated to Bessel Heat Equation

On the Operator k Related to Heat Equation

Local existence and blow up in a semilinear heat equation with the Bessel operator

In this work we consider an initial one-point boundary value problem to the heat equation with the Bessel operator ut − (uxx + 1 xux) = |u| p−2u. We first prove a local existence result. Then we show that the solution blows up in finite time.

On Generalization of Sturm-Liouville Theory for Fractional Bessel Operator

In this paper, we give the spectral theory for eigenvalues and eigenfunctions of a boundary value problem consisting of the linear fractional Bessel operator. Moreover, we show that this operator is self-adjoint, the eigenvalues of the problem are real, and the corresponding eigenfunctions are orthogonal. In this paper, we give the spectral theory for eigenvalues and eigenfunctions...

On the Diamond Bessel Heat Kernel

We study the heat equation in n dimensional by Diamond Bessel operator. We find the solution by method of convolution and Fourier transform in distribution theory and also obtain an interesting kernel related to the spectrum and the kernel which is called Bessel heat kernel.

On the Solution n-Dimensional of the Product ⊗k Operator and Diamond Bessel Operator

Firstly, we studied the solution of the equation ⊗♦Bu x f x where u x is an unknown unknown function for x x1, x2, . . . , xn ∈ R, f x is the generalized function, k is a positive integer. Finally, we have studied the solution of the nonlinear equation ⊗♦Bu x f x, LΔB kBu x . It was found that the existence of the solution u x of such an equation depends on the condition of f and LΔB kBu x . Mo...