In this paper, we study the global existence of steady subsonic Euler flows through infinitely long nozzles without the assumption of irrotationality. It is shown that when the variation of Bernoulli’s function in the upstream is sufficiently small and mass flux is in a suitable regime with an upper critical value, then there exists a unique global subsonic solution in a suitable class for a ge...

For quasilinear integro-diierential equations of the form u t ?aA(u) = f, where a is a scalar singular integral kernel that behaves like t ? , 1 2 < 1 and A is a second order quasilinear elliptic operator in divergence form, solutions are found for which A(u) is integrable over space and time.

Asymptotic forms are determined for positive solutions which are called weakly increasing solutions to quasilinear ordinary differential equations.

Contents. x1. The origin and nature of Schrr odinger type approximations. x2. Formulating the ansatz. x3. Equations for the prooles. x4. Solvability of the the proole equations. x5. Convergence towards exact solutions. x6. The quasilinear case.

All systems of (n+1)-dimensional quasilinear evolutional secondorder equations invariant under the chain of algebras AG(1.n) ⊂ AG1(1.n) ⊂ AG2(1.n) are described. The obtained results are illustrated by examples of nonlinear Schrödinger equations.

In the paper a Picone-type identity for half-linear differential equations of second order is derived and Sturmian theory for both forced and unforced halflinear and quasilinear equations based on this identity is developed.

we propose a new high-order approximation for the solution of two-space-dimensional quasilinear hyperbolic partial differential equation of the form utt A x, y, t, u uxx B x, y, t, u uyy g x, y, t, u, ux, uy, ut , 0 < x, y < 1, t > 0 subject to appropriate initial and Dirichlet boundary conditions , where k > 0 and h > 0 are mesh sizes in time and space directions, respectively. We use only fiv...

We introduce a new class of quasilinear nonlocal operators and study equations involving these operators. The operators are degenerate elliptic and may have arbitrary growth in the gradient. Included are new nonlocal versions of p-Laplace, ∞-Laplace, mean curvature of graph, and even strongly degenerate operators. Our main results are non-trivial comparison, uniqueness, and existence results fo...

In this paper we establish a geometric theory for abstract quasilinear parabolic equations. In particular, we study existence, uniqueness, and continuous dependence of solutions. Moreover, we give conditions for global existence and establish smoothness properties of solutions. The results are based on maximal regularity estimates in continuous interpolation spaces. An important new ingredient ...