ترغب بنشر مسار تعليمي؟ اضغط هنا

Global existence for a nonlocal model for adhesive contact

70   0   0.0 ( 0 )
 نشر من قبل Elena Bonetti
 تاريخ النشر 2017
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

In this paper we address the analytical investigation of a model for adhesive contact, which includes nonlocal sources of damage on the contact surface, such as the elongation. The resulting PDE system features various nonlinearities rendering the unilateral contact conditions, the physical constraints on the internal variables, as well as the integral contributions related to the nonlocal forces. For the associated initial-boundary value problem we obtain a global-in-time existence result by proving the existence of a local solution via a suitable approximation procedure and then by extending the local solution to a global one by a nonstandard prolongation argument.



قيم البحث

اقرأ أيضاً

143 - Yu Gao , Cong Wang , Xiaoping Xue 2020
In this paper, we study a one dimensional nonlinear equation with diffusion $- u(-partial_{xx})^{frac{alpha}{2}}$ for $0leq alphaleq 2$ and $ u>0$. We use a viscous-splitting algorithm to obtain global nonnegative weak solutions in space $L^1(mathbb{ R})cap H^{1/2}(mathbb{R})$ when $0leqalphaleq 2$. For subcritical $1<alphaleq 2$ and critical case $alpha=1$, we obtain global existence and uniqueness of nonnegative spatial analytic solutions. We use a fractional bootstrap method to improve the regularity of mild solutions in Bessel potential spaces for subcritical case $1<alphaleq 2$. Then, we show that the solutions are spatial analytic and can be extended globally. For the critical case $alpha=1$, if the initial data $rho_0$ satisfies $- u<infrho_0<0$, we use the characteristics methods for complex Burgers equation to obtain a unique spatial analytic solution to our target equation in some bounded time interval. If $rho_0geq0$, the solution exists globally and converges to steady state.
68 - Anup Biswas 2018
We consider a class of semilinear nonlocal problems with vanishing exterior condition and establish a Ambrosetti-Prodi type phenomenon when the nonlinear term satisfies certain conditions. Our technique makes use of the probabilistic tools and heat kernel estimates.
144 - Hiroki Yagisita 2008
We consider the nonlocal analogue of the Fisher-KPP equation. We do not assume that the Borel-measure is absolutely continuous with respect to the Lebesgue measure. We gives a sufficient condition for existence of traveling waves, and a necessary condition for existence of periodic traveling waves.
152 - Hiroki Yagisita 2016
We consider a nonlocal analogue of the Fisher-KPP equation. We do not assume that the Borel-measure for the convolution is absolutely continuous. In order to show the main result, we modify a recursive method for abstract monotone discrete dynamical systems by Weinberger. We note that the monotone semiflow generated by the equation does not have compactness with respect to the compact-open topology. At the end, we propose a discrete model that describes the measurement process.
151 - Ciprian G. Gal 2013
We investigate the long term behavior in terms of global attractors, as time goes to infinity, of solutions to a continuum model for biological aggregations in which individuals experience long-range social attraction and short range dispersal. We co nsider the aggregation equation with both degenerate and non-degenerate diffusion in a bounded domain subject to various boundary conditions. In the degenerate case, we prove the existence of the global attractor and derive some optimal regularity results. Furthermore, in the non-degenerate case we give a complete structural characterization of the global attractor, and also discuss the convergence of any bounded solutions to steady states. Finally, the existence of an exponential attractor is also demonstrated for sufficiently smooth kernels in the case of non-degenerate diffusion.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا