Identification of the Point Sources in Some Stochastic Wave Equations

Nonlinear stochastic wave equations

In this paper we study the Cauchy problem for the semilinear stochastic wave equation (@ 2

Parameter identification for deterministic and stochastic differential equations using the “collage method” for fixed point equations

Some linear fractional stochastic equations

Using the multiple stochastic integrals we prove an existence and uniqueness result for a linear stochastic equation driven by the fractional Brownian motion with any Hurst parameter. We study both the one parameter and two parameter cases. When the drift is zero, we show that in the one-parameter case the solution in an exponential, thus positive, function while in the two-parameter settings t...

Asymptotic Solutions of Semilinear Stochastic Wave Equations

Large-time asymptotic properties of solutions to a class of semilinear stochastic wave equations with damping in a bounded domain are considered. First an energy inequality and the exponential bound for a linear stochastic equation are established. Under appropriate conditions, the existence theorem for a unique global solution is given. Next the questions of bounded solutions and the exponenti...

extensions of some polynomial inequalities to the polar derivative

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