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On the Biharmonic Heat Equation on Complete Riemannian Manifolds
We study entire solutions of the biharmonic heat equation on complete Riemannian manifolds without boundary. We provide exponential decay estimates...
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Bubbling analysis for extrinsic biharmonic maps from general Riemannian 4-manifolds
In this paper, we study the blow-up analysis of extrinsic biharmonic maps from a general Riemannian 4-manifold into a compact Riemannian manifold. We...
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On Some Asymptotic Properties of Solutions to Biharmonic Equations
The author considers the application of the approximation theory methods to the principles of optimality in the decision-making theory. In finding...
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Dirichlet Problem for Inhomogeneous Biharmonic Equation in Clifford Analysis
An integral representation formula in terms of the bi-Laplacian operator is obtained and Dirichlet problem for the bi-Poisson equation is solved in...
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Neumann Eigenvalues of the Biharmonic Operator on Domains: Geometric Bounds and Related Results
We study an eigenvalue problem for the biharmonic operator with Neumann boundary conditions on domains of Riemannian manifolds. We discuss the weak...
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A stabilizer-free C0 weak Galerkin method for the biharmonic equations
In this article, we present and analyze a stabilizer-free C 0 weak Galerkin (SF-C0WG) method for solving the biharmonic problem. The SF-C0WG method is...
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Biharmonic systems involving a Rellich-type potential and multiple critical strongly coupled terms
In this work, we study the combined effect of concave and convex nonlinearities on the number of solutions for a biharmonic elliptic system involving...
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Sharp well-posedness of the biharmonic Schrödinger equation in a quarter plane
We obtain an almost sharp local well–posedness result for the biharmonic equation on the quarter plane. In addition, we prove that the nonlinear part...
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Unconditional optimal error bounds of the fast nonuniform Alikhanov scheme for a nonlinear time-fractional biharmonic equation
In this work, we will consider the two-dimensional nonlinear time-fractional biharmonic equation with weakly singular solutions. By introducing an...
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Well-Posedness and Asymptotic Behavior for the Dissipative p-Biharmonic Wave Equation with Logarithmic Nonlinearity and Dam** Terms
AbstractThis paper concerns with the initial and boundary value problem for a p -biharmonic wave equation with logarithmic nonlinearity and dam**...
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Nonlinear degenerate Navier problem involving the weighted biharmonic operator with measure data in weighted Sobolev spaces
In this paper, we prove the existence and uniqueness of weak solution for a nonlinear degenerate Navier problem involving the weighted biharmonic...
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Invertibility Criteria for the Biharmonic Single-Layer Potential
While the single-layer operator for the Laplacian is well understood, questions remain concerning the single-layer operator for the Bilaplacian,...
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Existence of Solutions for Biharmonic Equations on Conical Singular Manifolds
The manifolds with singularities are of great importance in geometric analysis. In general, the singularities include cones, edges, corners, or...