Blow-up rate for a semi-linear accretive wave equation

نویسنده

  • M. Jazar
چکیده

X iv :0 71 0. 13 61 v3 [ m at hph ] 1 6 O ct 2 00 7 Blow-up rate for a semi-linear accretive wave equation M. Jazar∗ and Ch. Messikh Abstract. In this paper we consider the semi-linear wave equation: utt − ∆u = ut|ut| in R where 1 ≤ p ≤ 1 + 4 N−1 if N ≥ 2. We give the optimal blow-up rate for blowing up solutions of this equation. AMS Subject Classifications: 35L05,35L67

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Optimal bounds and blow-up criteria for a semi-linear accretive wave equation

In this paper we consider the semi-linear wave equation: utt − ∆u = ut|ut| in R where 1 < p ≤ 1 + 2 N−1 and p < 3 if N = 1, p 6= 3 if N = 2. We give an energetic criteria and optimal lower bound for blowing up solutions of this equation.

متن کامل

Optimal bounds and blow-up criteria for a semi-linear wave equation with nonlinearity on the velocity

In this paper we consider the semi-linear wave equation: utt −∆u = ut|ut| in R where 1 < p ≤ 1 + 2 N−1 and p < 5 if N = 1, p 6= 3 if N = 2. We give an energetic criteria and optimal lower bound for blowing up solutions of this equation.

متن کامل

Local existence and uniqueness for a semi-linear accretive wave equation

We prove local existence and uniqueness of the solution (u, ut) ∈ C 0([0, T ];H1 × L2(RN )) of the semilinear wave equation utt −∆u = ut|ut| p−1 for 1 < p < 1 + 2 N .

متن کامل

Existence and blow-up of solution of Cauchy problem for the sixth order damped Boussinesq equation

‎In this paper‎, ‎we consider the existence and uniqueness of the global solution for the sixth-order damped Boussinesq equation‎. ‎Moreover‎, ‎the finite-time blow-up of the solution for the equation is investigated by the concavity method‎.

متن کامل

BLOW-UP AND NONGLOBAL SOLUTION FOR A FAMILY OF NONLINEAR HIGHER-ORDER EVOLUTION PROBLEM

In this paper we consider a kind of higher-order evolution equation as^{kt^{k} + ^{k&minus1}u/t^{k&minus1} +• • •+ut &minus{delta}u= f (u, {delta}u,x). For this equation, we investigate nonglobal solution, blow-up in finite time and instantaneous blow-up under some assumption on k, f and initial data. In this paper we employ the Test function method, the eneralized convexity method an...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2008