This paper is concerned with an inverse source problem for the stochastic biharmonic wave equation. The driven assumed to be a microlocally isotropic Gaussian random field its covariance operator being classical pseudo-differential operator. well-posedness of direct examined in distribution sense, and regularity solution discussed given rough source. For problem, strength source, involved princ...

In this study, we investigate the intial value problem (IVP) for a time-fractional fourth-order equation with nonlinear source terms. More specifically, consider biharmonic exponential nonlinearity and Cahn–Hilliard equation. By using Fourier transform concept, generalized formula mild solution as well smoothing effects of resolvent operators are proved. For IVP associated first one, by Orlicz ...

Let Ω be a bounded Lipschitz domain in Rn, n ≥ 3. Let L be a second order elliptic system with constant coefficients satisfying the Legendre-Hadamard condition. We consider the Dirichlet problem Lu = 0 in Ω, u = f on ∂Ω with boundary data f in the Morrey space L2,λ(∂Ω). Assume that 0 ≤ λ < 2 + ε for n ≥ 4 where ε > 0 depends on Ω, and 0 ≤ λ ≤ 2 for n = 3. We obtain existence and uniqueness resu...

We prove an apriori estimate in Morrey spaces for both intrinsic and extrinsic biharmonic maps into spheres. As applications, we prove an energy quantization theorem for biharmonic maps from 4-manifolds into spheres and a partial regularity for stationary intrinsic biharmonic maps into spheres. x