Keyword

weak solutions

Description: Solutions to differential equations that satisfy the equations in an integral or distributional sense, even when they lack classical differentiability.

Primary topic: Nonlinear Partial Differential Equations (28%)

Wikidata ID: wiki/Q7977966

OpenAlex ID: keywords/weak-solutions

High resolution schemes for hyperbolic conservation laws

1983 · Ami Harten · Journal of Computational Physics · 4,191

PDF

Second Order Parabolic Differential Equations

1996 · G M Lieberman · WORLD SCIENTIFIC eBooks · 1,988

Vorticity and Incompressible Flow

2001 · Andrew J. Majda, Andrea L. Bertozzi · Cambridge University Press eBooks · 1,917

Weak solutions of nonlinear hyperbolic equations and their numerical computation

1954 · Peter D. Lax · Communications on Pure and Applied Mathematics · 1,840

First Order Quasilinear Equations in Several Independent Variables

1970 · S N Kružkov · Mathematics of the USSR-Sbornik · 1,816

Regularity for a more general class of quasilinear elliptic equations

1984 · Peter Tolksdorf · Journal of Differential Equations · 1,492

PDF

On the Navier-Stokes initial value problem. I

1964 · Hiroshi Fujita, Tosio Kato · Archive for Rational Mechanics and Analysis · 1,294

On Elliptic Partial Differential Equations

2011 · L. Nirenberg · Springer eBooks · 1,293

StrongL p -solutions of the Navier-Stokes equation inR m , with applications to weak solutions

1984 · Tosio Kato · Mathematische Zeitschrift · 1,286

Boundary regularity for solutions of degenerate elliptic equations

1988 · Gary M. Lieberman · Nonlinear Analysis · 1,267

Generalized Solutions of Hamilton-Jacobi Equations

1982 · Pierre‐Louis Lions · Medical Entomology and Zoology · 1,245

Initial value/boundary value problems for fractional diffusion-wave equations and applications to some inverse problems

2011 · Kenichi Sakamoto, Masahiro Yamamoto · Journal of Mathematical Analysis and Applications · 1,207

Optimal Control of Partial Differential Equations

2010 · Fredi Tröltzsch · Graduate studies in mathematics · 1,177

A Strong Maximum Principle for some quasilinear elliptic equations

1984 · J. L. V�zquez · Applied Mathematics & Optimization · 1,161

Motion of level sets by mean curvature. I

1991 · L. C. Evans, J. Spruck · Journal of Differential Geometry · 1,160

PDF

An implicit finite-difference algorithm for hyperbolic systems in conservation-law form

1976 · Richard M Beam, R.F Warming · Journal of Computational Physics · 1,113

C1 + α local regularity of weak solutions of degenerate elliptic equations

1983 · E. DiBenedetto · Nonlinear Analysis · 1,098

Discontinuous dynamical systems

2008 · Jorge Cortes · IEEE Control Systems · 1,069

PDF

On the interior regularity of weak solutions of the Navier-Stokes equations

1962 · James Serrin · Archive for Rational Mechanics and Analysis · 1,002

Tensor Rank and the Ill-Posedness of the Best Low-Rank Approximation Problem

2008 · Vin de Silva, Lek-Heng Lim · SIAM Journal on Matrix Analysis and Applications · 927

PDF

Solutions for semilinear parabolic equations in Lp and regularity of weak solutions of the Navier-Stokes system

1986 · Yoshikazu Giga · Journal of Differential Equations · 867

PDF

On the Existence of Globally Defined Weak Solutions to the Navier—Stokes Equations

2001 · E. Feireisl, A. Novotný, et al. · Journal of Mathematical Fluid Mechanics · 853

Exact controllability and stabilization: The multiplier method

1994 · Vilmos Komornik · 821

Saddle points and instability of nonlinear hyperbolic equations

1975 · L. E. Payne, D. H. Sattinger · Israel Journal of Mathematics · 818

Regularity and existence of solutions of elliptic equations with p,q-growth conditions

1991 · Paolo Marcellini · Journal of Differential Equations · 816

PDF

Works count: 24,980

Citation count: 312,400