The dirichlet problem for the tricomi equation

A numerical experiment on a second‐order partial differential equation of mixed type

“…The successively higher curves have smaller spacing. We see that as the mesh is refined the energy absorption increases and approaches a limiting curve corresponding to the energy absorption for the solution of (8). It is apparent from Figure 3 that as c goes to zero A is approximately 0.04.…”

A Dual Variational Approach to a Class of Nonlocal Semilinear Tricomi Problems

“…First, one could equally well consider boundary conditions of Guderley-Morawetz type, in which data is placed on ∂Ω\Γ where Γ is a characteristic gap (cf. Theorems 1,2 of [17]), where the overdetermining nature of the hyperbolicity continues to be respected. On the other hand, a boundary condition of Dirichlet type on the entire boundary, which is natural for flows past profiles, involves the a priori treatment of singularities which must be present and hence the behavior of this linear problem is much less well understood (cf.…”

“…On the other hand, a boundary condition of Dirichlet type on the entire boundary, which is natural for flows past profiles, involves the a priori treatment of singularities which must be present and hence the behavior of this linear problem is much less well understood (cf. [17], [18]. Second, one could try to follow the path of variational methods for nonpotential operators (cf.…”

Existence and regularity of solution of mixed boundary value problem of a Busemann-equation with nonlinear absorb term

“…The Busemann-equation (see [1,2]) is the following equation u xx + y m u yy = f (x, y, u) (1.1) which is a classical equation coming from fluid dynamics. Busemann-equation is elliptic in y > 0 and is hyperbolic in y < 0, if m is odd.…”