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Design and analysis of efficient computational techniques for solving a temporal‐fractional partial differential equation with the weakly singular solution

Mathematical methods in the applied sciences, 2023
This work deals with the construction of robust numerical schemes for solving a time‐fractional convection‐diffusion (TFCD) equation with variable coefficients subject to weakly singular solution.
P. Roul
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Singularities of Solutions of Singular Integral Equations

Ukrainian Mathematical Journal, 2002
This paper deals with a singular integral equation \[ Sq+Tq=f,\tag{1} \] where \(q(x)\) is an unknown function, \[ Sq(x):=aq(x)+\frac{1}{\pi }\text{v.p.} \int_{-1}^{1} \frac{q(\tau)}{\tau -x} d\tau,\;Tq(x):=\int_{-1}^{1}K(x,\tau)q(\tau) d\tau. \] It is assumed that the functions \(f\) and \(K\) smoothly depend on additional parameters.
Kapustyan, V. E., Il'man, V. M.
openaire   +1 more source

Self-similar Singular Solution of a P-Laplacian Evolution Equation with Gradient Absorption Term

Journal of Partial Differential Equations, 2004
In this paper we deal with the self-similar singular solution of the p-Laplacian evolution equation ut = div(|△↓u|^p-2△↓u) -|△↓|^q for p > 2 and q > 1 in R^n× (0, ∞). We prove that when p > q + n/(n + 1) there exist self-similar singular solutions, while
P. Shi
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