Galerkin methods for multidimensional nonlinear Volterra type equations
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.
The paper deals with positive solutions of a nonlocal and degenerate quasilinear parabolic system not in divergence form 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 to this problem. Moreover, a necessary and sufficient condition for the non-global existence...