Daniel Toundykov

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Various subsurface flow systems exhibit a combination of small-scale to large-scale anisotropy in hydraulic conductivity (K). The large-scale anisotropy results from systematic trends (e.g., exponential decrease or increase) of K with depth. We present a general two-dimensional solution for calculation of topography-driven groundwater flow considering both(More)
Analytical models of groundwater flow with a spatially varying elevation of a top boundary are widely used. However, a vast majority of previous analytical studies truncated the irregularly shaped top section with little to no analyses of the shortcomings of the approximate solutions for the resulting rectangles or parallelepipeds. We present an analytical(More)
This paper settles a conjecture by Gazzola and Pavani [10] regarding solutions to the fourth order ODE w(4) + kw′′ + f (w) = 0 which arises in models of traveling waves in suspension bridges when k > 0. Under suitable assumptions on the nonlinearity f and initial data, we demonstrate blow-up in finite time. The case k ≤ 0 was first investigated by Gazzola(More)
We derive global in time a priori bounds on higherlevel energy norms of strong solutions to a semilinear wave equation: in particular, we prove that despite the influence of a nonlinear source, the evolution of a smooth initial state is globally bounded in the strong topology ∼ H × H. And the bound is uniform with respect to the corresponding norm of the(More)
Weak solutions and blow-up for wave equations of p-Laplacian type with supercritical sources" (2015). This paper investigates a quasilinear wave equation with Kelvin-Voigt damping, u t t − ∆ p u − ∆u t = f (u), in a bounded domain Ω ⊂ R 3 and subject to Dirichlét boundary conditions. The operator ∆ p , 2 < p < 3, denotes the classical p-Laplacian. The(More)
We study regular solutions to wave equations with super-critical source terms, e.g., of exponent p > 5 in 3D. Such high-order sources have been a major challenge in the investigation of finite-energy (H1 × L2) solutions to wave PDEs for many years. The well-posedness question has been answered in part, but even the local existence, for instance, in 3(More)
"Well-posedness and stability of a semilinear Mindlin-Timoshenko plate model" I will discuss well-posedness and long-time behavior of Mindlin-Timoshenko plate equations that describe vibrations of thin plates. This system of partial differential equations was derived by R. Mindlin in 1951 (though E. Reissner also considered an analogous model earlier in(More)
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