The Cauchy problem for effectively hyperbolic equations. A standard type

a cauchy-schwarz type inequality for fuzzy integrals

نامساوی کوشی-شوارتز در حالت کلاسیک در فضای اندازه فازی برقرار نمی باشد اما با اعمال شرط هایی در مسئله مانند یکنوا بودن توابع و قرار گرفتن در بازه صفر ویک می توان دو نوع نامساوی کوشی-شوارتز را در فضای اندازه فازی اثبات نمود.

A timelike Cauchy problem and an inverse problem for general hyperbolic equations

Stability of Entropy Solutions to the Cauchy Problem for a Class of Nonlinear Hyperbolic-Parabolic Equations

Consider the Cauchy problem for the nonlinear hyperbolic-parabolic equation: (*) ut + 1 2 a · ∇xu = ∆u+ for t > 0, where a is a constant vector and u+ = max{u, 0}. The equation is hyperbolic in the region [u < 0] and parabolic in the region [u > 0]. It is shown that entropy solutions to (*), that grow at most linearly as |x| → ∞, are stable in a weighted L(IR ) space, which implies that the sol...

Modified Decomposition Method for Solving the Cauchy Problem for Nonlinear Parabolic-Hyperbolic Equations

In this paper Modified decomposition method is applied to the solvability of nonlinear parabolic-hyperbolic equations and illustrated with a few simple examples.

THE CAUCHY PROBLEM FOR p-EVOLUTION EQUATIONS

In this paper we deal with the Cauchy problem for evolution equations with real characteristics. We show that the problem is well-posed in Sobolev spaces assuming a suitable decay of the coefficients as the space variable x → ∞. In some cases, such a decay may also compensate a lack of regularity with respect to the time variable t.