Some non-local problems for the parabolic-hyperbolic type equation with non-characteristic line of changing type

Nonexistence for mixed-type equations with critical exponent nonlinearity in a ball

“…In [1][2][3][4][5][10][11][12][13][14] and other papers, the existence and uniqueness of solutions for equations like (1.1) with linearities f (x, y, u) were obtained on kinds of domains with different boundary conditions. In these papers, the uniqueness was proved directly.…”

“…Tricomi problems and mixed-type equations like (1.1) with f (u) = 0 or f (u) = λu and other types have been widely considered (see [1][2][3][4][5][6][7][8][9][10][11][12][13][14]). The existence and uniqueness were obtained in these earlier papers under suitable conditions on different domains.…”

The loaded parabolic-hyperbolic equation and its relation to non-local problems

“…This subject has been studied extensively and has been developed by numerous mathematicians [12][13][14], due to, the increasing popularity of its connection with non-local problems, and the appearance of these PDEs in mathematical models for various problems which possess physical traits. For instance, while studying problems of moisture transfer in soils, heat transfer in heterogeneous media, diffusion of thermal neutrons in inhibitors, simulation of various biological processes, phenomena etc [6,[15][16][17][18].…”

On a nonlocal problem for mixed parabolic–hyperbolic type equation with nonsmooth line of type changing

“…Regarding the investigations mixed parabolic-hyperbolic equations with non-smooth lines of type changing we note works [11][12][13][14].…”

“…Omitting huge amount of works, related to the studying mixed type equations, we only note some recent works on local and non-local boundary problems for parabolic-hyperbolic equations [6][7][8][9][10].…”