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

author

  • Y. Wang School of Mathematical Sciences‎, ‎University of Electronic Science and Technology of China‎, ‎Chengdu 611731‎, ‎P.R‎. ‎China.
Abstract:

‎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.

Upgrade to premium to download articles

Sign up to access the full text

Already have an account?login

similar resources

Cauchy Problem for the Sixth-order Damped Multidimensional Boussinesq Equation

In this article, we consider the Cauchy problem for sixth-order damped Boussinesq equation in Rn. The well-posedness of global solutions and blow-up of solutions are obtained. The asymptotic behavior of the solution is established by the multiplier method.

full text

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...

full text

Blow up in the Cauchy problem for a nonlinearly damped wave equation

In this paper we consider the Cauchy problem for the nonlinearly damped wave equation with nonlinear source utt −∆u + aut|ut|m−2 = bu|u|p−2, p > m. We prove that given any time T > 0, there exist always initial data with sufficiently negative initial energy, for which the solution blows up in time ≤ T. This result improves an earlier one by Todorova [11].

full text

existence and approximate $l^{p}$ and continuous solution of nonlinear integral equations of the hammerstein and volterra types

بسیاری از پدیده ها در جهان ما اساساً غیرخطی هستند، و توسط معادلات غیرخطی ‎‏بیان شد‎‎‏ه اند. از آنجا که ظهور کامپیوترهای رقمی با عملکرد بالا، حل مسایل خطی را آسان تر می کند. با این حال، به طور کلی به دست آوردن جوابهای دقیق از مسایل غیرخطی دشوار است. روش عددی، به طور کلی محاسبه پیچیده مسایل غیرخطی را اداره می کند. با این حال، دادن نقاط به یک منحنی و به دست آوردن منحنی کامل که اغلب پرهزینه و ...

15 صفحه اول

Existence, global nonexistence, and asymptotic behavior of solutions for the Cauchy problem of a multidimensional generalized damped Boussinesq-type equation

where u (x, t) denotes the unknown function, f (s) is the given nonlinear function, u0 (x) and u1 (x) are the given initial value functions, k is a constant, the subscript t indicates the partial derivative with respect to t, n is the dimension of space variable x, and △ denotes the Laplace operator in R. The effects of small nonlinearity and dispersion are taken into consideration in the deriv...

full text

Validity of the Weakly-nonlinear Solution of the Cauchy Problem for the Boussinesq–ostrovsky Equation

We consider the initial-value problem for the regularized Boussinesq–Ostrovsky equation in the class of periodic functions. Validity of the weakly-nonlinear solution, given in terms of two counter-propagating waves satisfying the uncoupled Ostrovsky equations, is examined. We prove analytically and illustrate numerically that the improved accuracy of the solution can be achieved at the time sca...

full text

My Resources

Save resource for easier access later

Save to my library Already added to my library

{@ msg_add @}


Journal title

volume 43  issue 5

pages  1057- 1071

publication date 2017-10-01

By following a journal you will be notified via email when a new issue of this journal is published.

Hosted on Doprax cloud platform doprax.com

copyright © 2015-2023