Hadamard well-posedness for a hyperbolic equation of viscoelasticity with supercritical sources and damping

Presented here is a study of a viscoelastic wave equation with supercritical source and damping terms. We employ the theory of monotone operators and nonlinear semigroups, combined with energy methods to establish the existence of a unique local weak solution. In addition, it is shown that the solution depends continuously on the initial data and is global provided the damping dominates the source in an appropriate sense.Comment: The 2nd version includes a new proof of the energy identit

Global well -posedness for systems of nonlinear wave equations

This dissertation deals with the global well-posedness of the system of nonlinear wave equations [special characters omitted]in a bounded domain Ω ⊂ [special characters omitted], n = 1, 2, 3; with Dirichlét boundary conditions. The nonlinearities f1(u, v) and f2(u, v) act as a strong source in the system and the exponents of velocities are restricted to the range 0 \u3c m, r ≤ 1. The non-critical case 0 \u3c m, r \u3c 1 and the critical case m = r = 1 are analyzed in Chapter 2 and Chapter 3, respectively. Under some restrictions on the parameters in the system we obtain several results on the existence of local solutions, global solutions, and uniqueness. In addition, we prove that weak solutions to the system blow up in finite time whenever the initial energy is negative and the exponent the source term is more dominant than the exponents of both damping terms

Dominating Broadcasts in Fuzzy Graphs

Broadcasting problems in graph theory play a significant role in solving many complicated physical problems. However, in real life there are many vague situations that sometimes cannot be modeled using usual graphs. Consequently, the concept of a fuzzy graph GF:(V,σ,μ) has been introduced to deal with such problems. In this study, we are interested in defining the notion of dominating broadcasts in fuzzy graphs. We also show that, in a connected fuzzy graph containing more than one element in σ*, a dominating broadcast always exists, where σ* is {v∈V|σ(v)>0}. In addition, we investigate the relationship between broadcast domination numbers, radii, and domination numbers in a fuzzy graph as follows; γb(GF)≤min{r(GF),γ(GF)}, where γb(GF) is the broadcast domination number, r(GF) is the radius, and γ(GF) is domination numbers in fuzzy graph GF, with |σ*|>1