Parabolic equations with conservative nonlinear term and singular initial data

DOI10.1016/S0362-546X(96)00353-7zbMath0889.35048OpenAlexW2026785421MaRDI QIDQ4374205

Todor Gramchev, Lucio Cadeddu, Hebe A. Biagioni

Publication date: 18 June 1998

Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0362-546x(96)00353-7

zbMATH Keywords

regularityBurgers' equationsemilinear parabolic equationlocal and global solutionslifespan of the local solutions

Mathematics Subject Classification ID

Related Items (6)

The vanishing viscosity method for the sensitivity analysis of an optimal control problem of conservation laws in the presence of shocks ⋮ Quasiasymptotic analysis in Colombeau algebra ⋮ Nonlinear parabolic equations with regularized derivatives in Colombeau algebra ⋮ Semilinear parabolic equations involving measures and low regularity data ⋮ Singular asymptotic expansions and delta waves for Burgers' equation ⋮ PERTURBED SCHRÖDINGER EQUATION WITH SINGULAR POTENTIAL AND INITIAL DATA

Cites Work

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• Nonlinear parabolic equations involving measures as initial conditions
• Generalized solutions to Burgers' equation
• Generalized solutions to conservation laws
• The Navier-Stokes equation for an incompressible fluid in \(\mathbb{R}^ 2\) with a measure as the initial vorticity
• Nonvanishing singular parts of measure valued solutions for scalar hyperbolic equations
• Semilinear heat equations and the navier-stokes equation with distributions in new function spaces as initial data
• Degenerate parabolic equations with initial data measures
• Nonuniqueness and Uniqueness in the Initial-Value Problem for Burgers’ Equation

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