|کد مقاله||کد نشریه||سال انتشار||مقاله انگلیسی||ترجمه فارسی||نسخه تمام متن|
|6417094||1338528||2015||29 صفحه PDF||سفارش دهید||دانلود رایگان|
In this paper we study higher order weakly hyperbolic equations with time dependent non-regular coefficients. The non-regularity here means less than Hölder, namely bounded coefficients. As for second order equations in  we prove that such equations admit a 'very weak solution' adapted to the type of solutions that exist for regular coefficients. The main idea in the construction of a very weak solution is the regularisation of the coefficients via convolution with a mollifier and a qualitative analysis of the corresponding family of classical solutions depending on the regularising parameter. Classical solutions are recovered as limit of very weak solutions. Finally, by using a reduction to block Sylvester form we conclude that any first order hyperbolic system with non-regular coefficients is solvable in the very weak sense.
Journal: Journal of Differential Equations - Volume 259, Issue 11, 5 December 2015, Pages 5846-5874