On some singular systems of parabolic functional equations
We will prove existence of weak solutions of a system, containing non-local terms , .
On some stochastic parabolic differential equations in a Hilbert space.
On Spectrum and Riesz basis property for one-dimensional wave equation with Boltzmann damping∗
In this paper, we study the one-dimensional wave equation with Boltzmann damping. Two different Boltzmann integrals that represent the memory of materials are considered. The spectral properties for both cases are thoroughly analyzed. It is found that when the memory of system is counted from the infinity, the spectrum of system contains a left half complex plane, which is sharp contrast to the most results in elastic vibration systems that the vibrating dynamics can be considered from the vibration...
On Spectrum and Riesz basis property for one-dimensional wave equation with Boltzmann damping∗
In this paper, we study the one-dimensional wave equation with Boltzmann damping. Two different Boltzmann integrals that represent the memory of materials are considered. The spectral properties for both cases are thoroughly analyzed. It is found that when the memory of system is counted from the infinity, the spectrum of system contains a left half complex plane, which is sharp contrast to the most results in elastic vibration systems that the vibrating dynamics can be considered from the vibration...
On stability and growth of solutions for classes of initial and boundary value problems
On surrogate learning for linear stability assessment of Navier-Stokes equations with stochastic viscosity
We study linear stability of solutions to the Navier-Stokes equations with stochastic viscosity. Specifically, we assume that the viscosity is given in the form of a stochastic expansion. Stability analysis requires a solution of the steady-state Navier-Stokes equation and then leads to a generalized eigenvalue problem, from which we wish to characterize the real part of the rightmost eigenvalue. While this can be achieved by Monte Carlo simulation, due to its computational cost we study three surrogates...
On symmetric equilibrium of an isothermal gas with a free boundary and a body force.
On the age-dependent predator-prey model
The paper deals with the description of a model which is the synthesis of two classical models, the Lotka-Volterra and McKendrick-von Foerster models. The existence and uniqueness of the solution for the new population problem are proved, as well the asymptotic periodicity but under some simplifying assumptions.
On the approximation of elliptic operators with discontinuous coefficients
On the backward heat equation
On the backward heat problem: evaluation of the norm of .
On the backward parabolic equation: a critical survey of some current methods
On the behavior of a nonstationary Poiseuille solution as .
On the behavior of the interface separating fresh and salt groundwater in a heterogeneous coastal aquifer.
On the Boundary Behaviour of Partially Free Minimal Surfaces.
On the Cauchy problem for convolution equations
We consider one-parameter (C₀)-semigroups of operators in the space with infinitesimal generator of the form where G is an -valued rapidly decreasing distribution on ℝⁿ. It is proved that the Petrovskiĭ condition for forward evolution ensures not only the existence and uniqueness of the above semigroup but also its nice behaviour after restriction to whichever of the function spaces , , p ∈ [1,∞], , a ∈ ]0,∞[, or the spaces , q ∈ ]1,∞], of bounded distributions.
On the Cauchy problem for hyperbolic functional-differential equations
We consider the Cauchy problem for a nonlocal wave equation in one dimension. We study the existence of solutions by means of bicharacteristics. The existence and uniqueness is obtained in topology. The existence theorem is proved in a subset generated by certain continuity conditions for the derivatives.
On the Cauchy problem for linear partial differential-functional equations of first order
On the Cauchy problem for linear PDEs with retarded arguments at derivatives
We present an existence theorem for the Cauchy problem related to linear partial differential-functional equations of an arbitrary order. The equations considered include the cases of retarded and deviated arguments at the derivatives of the unknown function. In the proof we use Tonelli's constructive method. We also give uniqueness criteria valid in a wide class of admissible functions. We present a set of examples to illustrate the theory.
On the Cauchy problem for the equation of one-dimensional non-stationary filtration with non-continuous initial data