We investigate the well-posedness of a class of nonlinear dispersive waves on trees, in connection with the mathematical modeling of the human cardiovascular system. Specifically, we study the Benjamin-Bona-Mahony (BBM) equation, also known as the regularized long wave equation, posed on finite trees, together with standard junction and terminal boundary conditions. We prove that the Cauchy pro...

⋆ Work supported by the Department of Energy, contract DE–AC03–76SF00515. † Permanent Address: Department of Physics and Astronomy, San Francisco State University, San Francisco, CA 94132 ‡ Permanent Address: Department of Physics and Astronomy, Sonoma State University, Rohnert Park, CA 94928 § [email protected] We analyze the initial value problem for scalar fields obeying the Kl...

In a recent paper Chávez and Sahoo considered the functional equation f(ux− vy, uy + v(x+ y)) = f(x, y)f(u, v), which arose in a number theoretical context. Unfortunately one of their results is incorrect. Here we reconsider the equation on various domains. We observe that it is in fact a multiplicative Cauchy equation in disguise. We also point out some remaining open problems.

A Legendre multiwavelet based method is developed in this paper to solve second kind hypersingular integral equation by converting it into a Cauchy singular integro-differential equation. Multiscale representation of the singular and differential operators is obtained by employing Legendre multiwavelet basis. An estimate of the error of the approximate solution of the integral equation is obtai...

∂u ∂t = A ∂ 2 u ∂x2 , u(0, x) = g(x). Moreover, we consider a representation of the solution of this problem as a Poisson integral and study the Cauchy problem for the corresponding inhomogeneous equation. Bibliography: 22 titles.

In this paper, we establish the global well-posedness of the Cauchy problem for the Gross-Pitaevskii equation with an angular momentum rotational term in which the angular velocity is equal to the isotropic trapping frequency in the space R .

We apply the I-method to prove that the Cauchy problem of a higher-order Schrödinger equation is globally well-posed in the Sobolev space Hs(R) with s > 6/7.

We solve the Cauchy problem for the Korteweg–de Vries equation with steplike finite-gap initial conditions under the assumption that the perturbations have a given number of derivatives and moments finite.

We study the large time behavior of solutions of the Cauchy problem for a fast diiusion equation with a singular powerlike source. It is shown that the large time behavior is described by the similarity solution of related problem.

We consider the Cauchy problem for the Euler-Bernoulli equation of the vibrating beam and solve it in Gevrey classes under appropriate Levi conditions on the lower order terms.