Strong ergodic properties of a first-order partial differential equation

A method for solving first order fuzzy differential equation

First Order Partial Differential Equations

If T⃗ denotes a vector tangent to C at t,x,u then the direction numbers of T⃗ must be a,b, f. But then (1.2) implies that T⃗ n⃗, which is to say, T⃗ lies in the tangent plane to the surface S. But if T⃗ lies in the tangent plane, then C must lie in S. Evidently, solution curves of (1.2) lie in the solution surface S associated with (1.2). Such curves are called characteristic curves for (1.2). W...

First order partial differential equations∗

2 Separation of variables and the complete integral 5 2.1 Separation of variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 The envelope of a family of curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.3 The complete integral . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.4 Determining the characteristic strips from t...

a method for solving first order fuzzy differential equation

Existence and strong pre-compactness properties for entropy solutions of a first-order quasilinear equation

Sequences of entropy solutions of a non-degenerate first-order quasilinear equation are shown to be strongly pre-compact in the general case of a Caratheodory flux vector. Existence of the weak and entropy solution to Cauchy problem for such equation is also established. The proofs are based on general localization principle for H-measures corresponding to sequences of measure-valued functions....