Principal eigenvalue of mixed problem for the fractional Laplacian: Moving the boundary conditions
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DOI: 10.1016/j.jde.2018.03.001
Abstract: Abstract We analyze the behavior of the eigenvalues of the following nonlocal mixed problem { ( − Δ ) s u = λ 1 ( D ) u in Ω , u = 0 in … read more here.
Keywords: eigenvalue mixed; fractional laplacian; problem fractional; mixed problem ... See more keywords
Classical solution of the first mixed problem for second-order hyperbolic equation in curvilinear half-strip with variable coefficients
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DOI: 10.1134/s0012266117010074
Abstract: The classical solution of the first mixed problem for a second-order hyperbolic equation with variable coefficients in the case of two independent variables in a curvilinear half-strip is considered. The existence and uniqueness of the… read more here.
Keywords: first mixed; problem second; solution first; solution ... See more keywords
Cauchy Problem and the Second Mixed Problem for Parabolic Equations with a Dirac Potential Concentrated at Finitely Many Given Points
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DOI: 10.1134/s001226611903008x
Abstract: We prove the existence and uniqueness of a classical solution of the Cauchy problem and the second mixed problem for parabolic equations whose potential is a linear combination of values of this solution at finitely… read more here.
Keywords: problem; problem parabolic; mixed problem; problem second ... See more keywords
Fourier Method for a Mixed Problem with the Hill Operator
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DOI: 10.1134/s0012266120060014
Abstract: Abstract Boundary value problems for a second-order ordinary differential equation with a nonsmooth potential are considered. An asymptotic representation for an operator semigroup is established based on a previously derived theorem on the eigenvalue asymptotics… read more here.
Keywords: hill operator; mixed problem; operator; fourier method ... See more keywords
Mixed Problem for a Homogeneous Wave Equation with a Nonzero Initial Velocity
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DOI: 10.1134/s0965542518090099
Abstract: A mixed problem for a homogeneous wave equation with fixed ends, a summable potential, and a nonzero initial velocity is studied. Using the resolvent approach and developing the Krylov method for accelerating the convergence of… read more here.
Keywords: homogeneous wave; velocity; problem homogeneous; initial velocity ... See more keywords
Mixed problem for the wave equation with a summable potential and nonzero initial velocity
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DOI: 10.1134/s106456241703022x
Abstract: The resolvent approach in the Fourier method, combined with Krylov’s ideas concerning convergence acceleration for Fourier series, is used to obtain a classical solution of a mixed problem for the wave equation with a summable… read more here.
Keywords: summable potential; problem wave; equation summable; mixed problem ... See more keywords
On the Solvability of a Mixed Problem for a High-Order Partial Differential Equation with Fractional Derivatives with Respect to Time, with Laplace Operators with Spatial Variables and Nonlocal Boundary Conditions in Sobolev Classes
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DOI: 10.3390/math7030235
Abstract: In this paper, we study the solvability of a mixed problem for a high-order partial differential equation with fractional derivatives with respect to time, and with Laplace operators with spatial variables and nonlocal boundary conditions… read more here.
Keywords: problem high; order partial; solvability mixed; partial differential ... See more keywords