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

Abstract

a b s t r a c tIn this work, we consider the following isotropic mixed-type equations:By proving some Pohozaev-type identities for (0.1) and dividing B r (0) naturally into six regions Ω i (i = 1, 2, 3, 4, 5, 6), we can show that the equationwith Dirichlet boundary conditions on each natural domain Ω i has no nontrivial regular solution in B r (0).

Existence of solutions to nonlinear advection-diffusion equation applied to Burgers’ equation using Sinc methods

“…With regard to the velocity field of a fluid, the essential ingredient of (1.4) in this study is the competition between the dissipative term εu xx the coefficient of which is the kinematic viscosity, and the nonlinear term uu x . Equation (1.4) appears as a mathematical model for many physical events such as gas dynamics, turbulence, and shock wave theory [6]. Many researchers have used various numerical methods to solve Burgers' equation [8], [4], [7].…”