-adic difference-difference Lotka-Volterra equation and ultra-discrete limit.
Parabolic differential-functional inequalities in viscosity sense
We consider viscosity solutions for second order differential-functional equations of parabolic type. Initial value and mixed problems are studied. Comparison theorems for subsolutions, supersolutions and solutions are considered.
Parabolic equations with deviating argument in advance
Partial differential equations with piecewise constant delay.
Peano type theorem for abstract parabolic equations
Periodic solutions for some partial functional differential equations.
Periodic solutions for some partial neutral functional differential equations.
Periodic solutions of abstract and partial differential equations with deviation
Perturbation theory for random walk in asymmetric random environment.
Propagation of weak discontinuities for quasilinear hyperbolic systems with coefficients functionally dependent on solutions
The propagation of weak discontinuities for quasilinear systems with coefficients functionally dependent on the solution is studied. We demonstrate that, similarly to the case of usual quasilinear systems, the transport equation for the intensity of weak discontinuity is quadratic in this intensity. However, the contribution from the (nonlocal) functional dependence appears to be in principle linear in the jump intensity (with some exceptions). For illustration, several examples, including two hyperbolic...