Howard A. Levine

Research.com Recognitions

• 2015 - Fellow of the American Association for the Advancement of Science (AAAS)
• 2013 - Fellow of the American Mathematical Society
• 1954 - Fellow of John Simon Guggenheim Memorial Foundation

Overview

Best Publications

• Instability and nonexistence of global solutions to nonlinear wave equations of the form _{}=-+ℱ()

  Howard A. Levine

  1108
  Citations

• The Role of Critical Exponents in Blowup Theorems

  Unknown

  899
  Citations

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

  Howard A. Levine

  775
  Citations

• The Role of Critical Exponents in Blow-Up Theorems: The Sequel

  Keng Deng;Howard A. Levine

  713
  Citations

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

  Howard A. Levine

  508
  Citations

• Mathematical Modeling of Capillary Formation and Development in Tumor Angiogenesis: Penetration into the Stroma

  Howard A. Levine;Serdal Pamuk;Brian D. Sleeman;Marit Nilsen-Hamilton

  336
  Citations

• A system of reaction diffusion equations arising in the theory of reinforced random walks

  Howard A. Levine;Brian D. Sleeman

  335
  Citations

• Global Nonexistence Theorems for Quasilinear Evolution Equations with Dissipation

  Howard A. Levine;James Serrin

  320
  Citations

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

  Howard A. Levine;Lawrence E. Payne

  283
  Citations

• On the existence and nonexistence of global solutions of reaction-diffusion equations in sectorial domains

  Catherine Bandle;Howard A. Levine

  217
  Citations

• A mathematical model for the roles of pericytes and macrophages in the initiation of angiogenesis. I. The role of protease inhibitors in preventing angiogenesis.

  Howard A. Levine;Brian D. Sleeman;Marit Nilsen-Hamilton

  216
  Citations

• Quenching, nonquenching, and beyond quenching for solution of some parabolic equations

  Howard A. Levine

  209
  Citations

• Global existence and global nonexistence of solutions of the Cauchy problem for a nonlinearly damped wave equation

  Howard A Levine;Sang Ro Park;James Serrin

  202
  Citations

• Mathematical modeling of the onset of capillary formation initiating angiogenesis

  Howard A. Levine;Brian D. Sleeman;Marit Nilsen-Hamilton

  191
  Citations

• A general approach to critical Fujita exponents in nonlinear parabolic problems

  Victor A. Galaktionov;Howard A. Levine

  187
  Citations

• On critical Fujita exponents for heat equations with nonlinear flux conditions on the boundary

  Victor A. Galaktionov;Howard A. Levine

  182
  Citations

• Critical blowup and global existence numbers for a weakly coupled system of reaction-diffusion equations

  Unknown

  153
  Citations

• Some existence and nonexistence theorems for solutions of degenerate parabolic equations

  Howard A Levine;Paul E Sacks

  141
  Citations

• Nonexistence of global weak solutions to some properly and improperly posed problems of mathematical physics: The method of unbounded fourier coefficients

  Howard A. Levine

  136
  Citations

• Blow up of solutions of the Cauchy problem for a wave equation with nonlinear damping and source terms and positive initial energy

  Howard A. Levine;Grozdena Todorova;Grozdena Todorova

  134
  Citations

• ON CRITICAL EXPONENTS FOR A SYSTEM OF HEAT EQUATIONS COUPLED IN THE BOUNDARY CONDITIONS

  K. Deng;M. Fila;H. A. Levine

  118
  Citations

• Non-existence, instability, and growth theorems for solutions of a class of abstract nonlinear equations with applications to nonlinear elastodynamics

  R. J. Knops;R. J. Knops;R. J. Knops;H. A. Levine;H. A. Levine;H. A. Levine;L. E. Payne;L. E. Payne;L. E. Payne

  102
  Citations