Nonexistence theorems for the heat equation with nonlinear boundary conditions and for the porous medium equation backward in time

Instability and nonexistence of global solutions to nonlinear wave equations of the form 𝑃𝑢_{𝑡𝑡}=-𝐴𝑢+ℱ(𝓊)

Howard A. Levine · Transactions of the American Mathematical Society · 1974 · 700 citations · Full text

Natural Sciences, Mathematics, Physics +17

Some nonexistence and instability theorems for solutions of formally parabolic equations of the form Put=−Au+ℱ(u)

Howard A. Levine · Archive for Rational Mechanics and Analysis · 1973 · 577 citations

Natural Sciences, Mathematics, Physics +10

Some Additional Remarks on the Nonexistence of Global Solutions to Nonlinear Wave Equations

Howard A. Levine · SIAM Journal on Mathematical Analysis · 1974 · 398 citations

Natural Sciences, Mathematics, Dynamical Systems +8

DIFFUSION FROM AN INSTANTANEOUS POINT SOURCE WITH A CONCENTRATION-DEPENDENT COEFFICIENT

R. E. Pattle · The Quarterly Journal of Mechanics and Applied Mathematics · 1959 · 395 citations

Engineering, Chemical Engineering, Chemical Kinetics +10

Regularity Propeties of Flows Through Porous Media

D. G. Aronson · SIAM Journal on Applied Mathematics · 1969 · 275 citations

Engineering, Physics, Fluid Dynamics +15