On a class of initial-boundary value problems in a domain with boundary containing isolated points
On a class of mixed boundary value problems for linear hyperbolic equations
On a fourth order equation in 3-D
In this article we study the positivity of the 4-th order Paneitz operator for closed 3-manifolds. We prove that the connected sum of two such 3-manifold retains the same positivity property. We also solve the analogue of the Yamabe equation for such a manifold.
On a Fourth Order Equation in 3-D
In this article we study the positivity of the 4-th order Paneitz operator for closed 3-manifolds. We prove that the connected sum of two such 3-manifold retains the same positivity property. We also solve the analogue of the Yamabe equation for such a manifold.
On a functional differential equation arising in the theory of the distribution of wealth.
On a nonlocal Ostrovsky-Whitham type dynamical system, its Riemann type inhomogeneous regularizations and their integrability.
On a shock problem involving a nonlinear viscoelastic bar.
On a Volterra Stieltjes integral equation.
On a Whitham-type equation.
On an equation with partial derivations in four-dimensional Euclidean space.
On analytic solutions to the generalized Cauchy problem with data on three surfaces for a quasilinear system.
On Asymptotic Behavior of Solution for the Navier-Stokes Equations in a Time Dependent Domain.
On blow-up of solution for Euler equations
We present numerical evidence for the blow-up of solution for the Euler equations. Our approximate solutions are Taylor polynomials in the time variable of an exact solution, and we believe that in terms of the exact solution, the blow-up will be rigorously proved.
On blow-up of solution for Euler equations
We present numerical evidence for the blow-up of solution for the Euler equations. Our approximate solutions are Taylor polynomials in the time variable of an exact solution, and we believe that in terms of the exact solution, the blow-up will be rigorously proved.
On Borel summable solutions of the multidimensional heat equation
We give a new characterisation of Borel summability of formal power series solutions to the n-dimensional heat equation in terms of holomorphic properties of the integral means of the Cauchy data. We also derive the Borel sum for the summable formal solutions.
On boundary integral equations of the first kind for the bi-laplacian in a polygonal plane domain
On closed-form solutions of some nonlinear partial differential equations.
On exact solutions of a degenerate quasilinear wave equation with source term.
On explicit and numerical solvability of parabolic initial-boundary value problems.
On generalized heat polynomials.