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Generalized Convolution Transforms and Toeplitz Plus Hankel Integral Equations

Xuan Thao, Nguyen, Kim Tuan, Vu, Thanh Hong, Nguyen (2008)

Fractional Calculus and Applied Analysis

Mathematics Subject Classification: 44A05, 44A35With the help of a generalized convolution and prove Watson’s and Plancherel’s theorems. Using generalized convolutions a class of Toeplitz plus Hankel integral equations, and also a system of integro-differential equations are solved in closed form.

Global and non-global existence of solutions to a nonlocal and degenerate quasilinear parabolic system

Yujuan Chen (2010)

Czechoslovak Mathematical Journal

The paper deals with positive solutions of a nonlocal and degenerate quasilinear parabolic system not in divergence form u t = v p Δ u + a Ω u d x , v t = u q Δ v + b Ω v d x with null Dirichlet boundary conditions. By using the standard approximation method, we first give a series of fine a priori estimates for the solution of the corresponding approximate problem. Then using the diagonal method, we get the local existence and the bounds of the solution ( u , v ) to this problem. Moreover, a necessary and sufficient condition for the non-global existence...

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