Buckling Eigenvalues for a Clamped Plate Embedded in an Elastic Medium and Related Questions

This paper considers the dependence of the sum of the first m eigenvalues of three classical problems from linear elasticity on a physical parameter in the equation. The paper also considers eigenvalues $\gamma _i (a)$ of a clamped plate under compression, depending on a lateral loading parameter $a;\Lambda i(a)$, the Dirichlet eigenvalues of the elliptic system describing linear elasticity depending on a combination a of the Lame constants, and eigenvalues $\Gamma _i (a)$ of a clamped vibrating plate under tension, depending on the ratio a of tension and flexural rigidity. In all three cases $a \in [0,\infty )$. The analysis of these eigenvalues and their dependence on a gives rise to some general considerations on singularly perturbed variational problems

Quenching for Quasilinear Equations

This is an Accepted Manuscript of an article published by Taylor & Francis as Marek, Fila, Bernhard Kawohl, and Howard A. Levine. "Quenching for Quasilinear Equations." Communications in Partial Differential Equations 17, no. 3-4 (1992): 593-614. Available online: https://doi.org/10.1080/03605309208820855. Posted with permission.</p

Quenching for Quasilinear Equations

This is an Accepted Manuscript of an article published by Taylor & Francis as Marek, Fila, Bernhard Kawohl, and Howard A. Levine. "Quenching for Quasilinear Equations." Communications in Partial Differential Equations 17, no. 3-4 (1992): 593-614. Available online: https://doi.org/10.1080/03605309208820855. Posted with permission.</p

Buckling Eigenvalues for a Clamped Plate Embedded in an Elastic Medium and Related Questions

This paper considers the dependence of the sum of the first m eigenvalues of three classical problems from linear elasticity on a physical parameter in the equation. The paper also considers eigenvalues $\gamma _i (a)$ of a clamped plate under compression, depending on a lateral loading parameter $a;\Lambda i(a)$, the Dirichlet eigenvalues of the elliptic system describing linear elasticity depending on a combination a of the Lame constants, and eigenvalues $\Gamma _i (a)$ of a clamped vibrating plate under tension, depending on the ratio a of tension and flexural rigidity. In all three cases $a \in [0,\infty )$. The analysis of these eigenvalues and their dependence on a gives rise to some general considerations on singularly perturbed variational problems.This is an article from SIAM Journal on Mathematical Analysis 24 (1993): 327, doi:10.1137/0524022. Posted with permission.</p