Existence and stability results of a nonlinear Timoshenko equation with damping and source terms

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 ...

Cauchy problem for a nonlinear wave equation with nonlinear damping and source terms

Here a; b¿0 and p¿1, m¿1. In case of IBVP, in a bounded domain ⊂Rn with Dirichlet boundary conditions, the following results are known: 1. When a=0, it is proved (see [1, 3, 8, 14, 16]) that the solution blows up in nite time for su ciently large initial data. 2. When b=0; Haraux and Zuazua [5] and Kopackova [7] prove the global existence result for large initial data. The behavior of the solut...

Global Existence and Nonexistence for Nonlinear Wave Equations with Damping and Source Terms

We consider an initial-boundary value problem for a nonlinear wave equation in one space dimension. The nonlinearity features the damping term |u|m−1 ut and a source term of the form |u|p−1 u, with m, p > 1. We show that whenever m ≥ p, then local weak solutions are global. On the other hand, we prove that whenever p > m and the initial energy is negative, then local weak solutions cannot be gl...

Mildly dissipative nonlinear Timoshenko systems — global existence and exponential stability

On Nonlinear Wave Equations with Degenerate Damping and Source Terms

In this article we focus on the global well-posedness of the differential equation utt − ∆u+ |u|k∂j(ut) = |u|p−1u in Ω× (0, T ), where ∂j is a sub-differential of a continuous convex function j. Under some conditions on j and the parameters in the equations, we obtain several results on the existence of global solutions, uniqueness, nonexistence and propagation of regularity. Under nominal assu...