Sentence examples for a regular solution for from inspiring English sources

The present paper is concerned with a Cauchy problem for a semilinear heat equation (P ut= Δu+upin RN× 0,∞),u x,0)="u0 x)⩾0in RN.We show that if p>N−2√N−1N−4−2√N−1 and N⩾11, then there exists a solution ui(i= 1,2,3) of (P) which blows up at t="Ti<+∞, becomes a regular solution for all t>Ti and behaves as follows:.

If for any, there exists a regular solution of ( 1.1 ) which satisfies boundary condition ( 1.2 ) in the sense that (14).

Let u ( x, t ) be a regular solution of (1 -(4).

With the aid of the assessed thermodynamic data (Li et al., 2004), the binary phase diagram of the Al Au system is reconstructed by assuming a regular solution model for the intermetallic Al2Au phase.

In this paper, our goal is to show the existence of a unique regular solution for this problem.

Then the boundary value problem (3.19), (3.20) has a unique regular solution for every (f(t)in L_{2} (mathbb{R}_ ;H )).

Uniqueness is proved for a regular solution.

(b) We establish now the existence of a regular solution ϱ to the transport equation (18) for a smooth initial density (rho ^{(varepsilon)}_{0}in C^{infty} overline{Omega})) such that (rho^leqvarrho ^{(varepsilon)}_{0}(x leq rho^).

We prove that there exists a unique global piecewise regular solution for piecewise regular initial density with bounded jump discontinuity.

In Section 2, the main results about the existence, regularity and dynamical behaviors of global piecewise regular solution for compressible Navier-Stokes equations are stated.

Li and Olver [3] studied the well-posedness, blow-up and the low regular solutions for an integrable nonlinearly dispersive model wave equation.