کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
839806 1470491 2014 43 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Almost global solutions of semilinear wave equations with the critical exponent in high dimensions
موضوعات مرتبط
مهندسی و علوم پایه سایر رشته های مهندسی مهندسی (عمومی)
پیش نمایش صفحه اول مقاله
Almost global solutions of semilinear wave equations with the critical exponent in high dimensions
چکیده انگلیسی

We are interested in the “almost” global-in-time existence of classical solutions in the general theory for nonlinear wave equations. All the three such cases are known to be sharp due to blow-up results in the critical case for model equations. However, it is known that we have a possibility to get the global-in-time existence for two of them in low space dimensions if the nonlinear term is of derivatives of the unknown function and satisfies the so-called null condition, or non-positive condition. But another one for the quadratic term in four space dimensions is out of the case as the nonlinear term should include a square of the unknown function itself.In this paper, we get one more example guaranteeing the sharpness of the almost global-in-time existence in four space dimensions. It is also the first example of the blow-up of classical solutions for non-single and indefinitely signed term in high dimensions. Such a term arises from the neglect of derivative-loss factors in Duhamel’s formula for positive and single nonlinear term. This fact may help us to describe a criterion to get the global-in-time existence in this critical situation.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Nonlinear Analysis: Theory, Methods & Applications - Volume 109, November 2014, Pages 187–229
نویسندگان
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