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Moreover, to obtain the time-decay rate in L q norm of solutions in Theorem 1.1, we first find the Green’s matrix for the linear system using the Fourier transform and then obtain

Then the change of variables, or area formula holds for f provided removing from counting into the multiplicity function the set where f is not approximately H¨ older continuous1.

Key words: Benjamin-Ono equation, time local well-posedness, smoothing effect.. ∗ Faculty of Education and Culture, Miyazaki University, Nishi 1-1, Gakuen kiharudai, Miyazaki

We describe the close connection between the linear system for the sixth Painlev´ e equation and the general Heun equation, formulate the Riemann–Hilbert problem for the Heun

Nonlinear systems of the form 1.1 arise in many applications such as the discrete models of steady-state equations of reaction–diffusion equations see 1–6, the discrete analogue of

In [9] a free energy encoding marked length spectra of closed geodesics was introduced, thus our objective is to analyze facts of the free energy of herein comparing with the

Among applications of the Carleman estimates obtained in this paper, we mention the sharp unique continuation/conditional stability results for the Cauchy problem for (1.1), the

In order to achieve the minimum of the lowest eigenvalue under a total mass constraint, the Stieltjes extension of the problem is necessary.. Section 3 gives two discrete examples