A Bäcklund transformation(BT) and a recurrence formula are derived by the homogeneous balance(HB) method. A initial problem of Burgers equations is reduced to a initial problem of heat equation by the BT, the initial problem of heat equation is resolved by the Fourier transformation method, substituting various solutions of the initial problem of the heat equation will yield solutions of the in...

The complex method of interpolation, going back to Calderón and Coifman et al., on the one hand, and the Alexander–Wermer–Slodkowski theorem on polynomial hulls with convex fibers, on the other hand, are generalized to a method of interpolation of real (finite-dimensional) Banach spaces and of convex functions. The underlying duality in this method is given by the Legendre transform. Our result...

We consider the class of non-negative rank-one convex isotropic integrands on \(\mathbb {R}^{n\times n}\) which are also positively p-homogeneous. If \(p\le n=2\) we prove, conditional quasiconvexity Burkholder integrand, that in this quasiconvex at conformal matrices. \(p\ge n =2\), show positive part integrand is polyconvex. In general, for n\), prove above polyconvex Several examples imply o...

The paper deals with the spatially homogeneous Boltzmann equation for hard potentials. An example is given which shows that, even though it is known that there is only one solution that conserves energy, there may be other solutions for which the energy is increasing; uniqueness holds if and only if energy is assumed to be conserved