In this paper we considered the semi-linear equation of mixed type of second kind, k(x, y)u_{tt} + u_{xx} + a(x, y)u_t + P(x, y)u_t + y(x, y)u - |u|^pu = f(z,y) For the above equation, we solved the modified Tricomi problem and have proved the existence and uniqueness of strong solution in H_1.

In this paper we offer a general method or constructing symmetries and conserved quantities in the (1 + 1)-dimensional integrable system, prove the algebraic relations between symmetries, and what is more, give applications of this method in many integrable systems with physical significance.

The solutions of the initial boundary value problems or the Navier-Stokes equations are constructed by means of a viscosity splitting scheme. Convergence results are proved.

In this paper we study the first boundary value problem for nonlinear diffusion equation \frac{∂u}{∂t} + \frac{∂}{∂x}f(u) = \frac{∂}{∂x}A(\frac{∂}{∂x}B(u)) whereA(s) = ∫¹_0a(σ)dσ, B(s) = ∫¹_0b(σ)dσ with a(s) ≥ 0, b(s) ≥ 0. We prove the existence of BV solutions under the much general structural conditions lim_{s → + ∞} A(s) = +∞, lim_{s → - ∞} A(s) = -∞ Moreover, we show the uniqueness without any structural conditions.

ln this paper, the order of magnitude and structure of nonnegative solutions for a class of R-D systems with 3 components is obtained. Especially for the case α_2 =α_3 a complete analysis is given. By using different method from [1], a simpler and more concrete sufficient condition for uniqueness and globally asymptotic stability of nonnegative solution is also obtained.

In this paper, first a class of Hirota-type equations Σ^l_{k=1}H_k(D_x,D_t,D_y)[F_k(D_x,D_t,D_y)f • f] • [G_k(D_x,D_t,D_y)f • f] = 0 are considered. By imposing certain conditions on F_k,G_k and H_k, we show that the abovementioned equation possesses one-soliton solution. Secondly we present a new integrable equation which is an extention of Novikov-Veselov equation and Ito equation. We obtain a Băcklund transformation (BT) of this equation. Finally we consider a generalized equation of Ramani and Sawada-Kotera, and obtain its BT. Starting with the BT an infinite number of conservation laws are derived.