On the blow-up scenario for some modified Serre–Green–Naghdi equations
نویسندگان
چکیده
The present paper deals with a modified Serre–Green–Naghdi (mSGN) system that has been introduced by Clamond et al. (2017) to improve the dispersion relation. We precise blow-up scenario of mSGN equations and we prove existence class solutions develop singularities in finite time. All presented results hold, same proof, for surface tension.
منابع مشابه
Blow-up Conditions for Two Dimensional Modified Euler-poisson Equations
The multi-dimensional Euler-Poisson system describes the dynamic behavior of many important physical flows, yet as a hyperbolic system its solution can blow-up for some initial configurations. This article strives to advance our understanding on the critical threshold phenomena through the study of a two-dimensional modified EulerPoisson system with a modified Riesz transform where the singular...
متن کاملA note on critical point and blow-up rates for singular and degenerate parabolic equations
In this paper, we consider singular and degenerate parabolic equations$$u_t =(x^alpha u_x)_x +u^m (x_0,t)v^{n} (x_0,t),quadv_t =(x^beta v_x)_x +u^q (x_0,t)v^{p} (x_0,t),$$ in $(0,a)times (0,T)$, subject to nullDirichlet boundary conditions, where $m,n, p,qge 0$, $alpha, betain [0,2)$ and $x_0in (0,a)$. The optimal classification of non-simultaneous and simultaneous blow-up solutions is determin...
متن کاملglobal results on some nonlinear partial differential equations for direct and inverse problems
در این رساله به بررسی رفتار جواب های رده ای از معادلات دیفرانسیل با مشتقات جزیی در دامنه های کراندار می پردازیم . این معادلات به فرم نیم-خطی و غیر خطی برای مسایل مستقیم و معکوس مورد مطالعه قرار می گیرند . به ویژه، تاثیر شرایط مختلف فیزیکی را در مساله، نظیر وجود موانع و منابع، پراکندگی و چسبندگی در معادلات موج و گرما بررسی می کنیم و به دنبال شرایطی می گردیم که متضمن وجود سراسری یا عدم وجود سراسر...
Blow - up Solutions for Gkdv Equations with K Blow
In this paper we consider the slightly L-supercritical gKdV equations ∂tu + (uxx + u|u|)x = 0, with the nonlinearity 5 < p < 5 + ε and 0 < ε ≪ 1 . In the previous paper [10] we know that there exists an stable selfsimilar blow-up dynamics for slightly L-supercritical gKdV equations. Such solution can be viewed as solutions with single blow-up point. In this paper we will prove the existence of ...
متن کاملBlow-up Results for Nonlinear Parabolic Equations on Manifolds
1. Introduction. The aim of this paper is threefold. First, by a unified approach, we prove that several classical blow-up results obtained over the last three decades for semilinear and quasilinear parabolic problems in R n are valid on noncompact, complete Riemannian manifolds, which include those with nonnegative Ricci curvatures. Next, we remove some unnecessary a priori growth conditions o...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Nonlinear Analysis-theory Methods & Applications
سال: 2022
ISSN: ['1873-5215', '0362-546X']
DOI: https://doi.org/10.1016/j.na.2022.113084