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The occurrence of collapse for quasilinear equations of parabolic and hyperbolic types

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Outgoing claims: the papers this work cites, builds on, or argues with.

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On solutions of nonlinear wave equations
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On the growth of solutions of quasi‐linear parabolic equations
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Finitely many mass points on the line under the influence of an exponential potential -- an integrable system
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Stability of nonlinear hyperbolic equations
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Existence and nonexistence in the large of solutions of quasilinear wave equations
inferredcites →https://doi.org/10.1007/bf00263041openalex-snapshot
Some nonexistence and instability theorems for solutions of formally parabolic equations of the form Put=−Au+ℱ(u)
inferredcites →https://doi.org/10.1007/bf00282433openalex-snapshot
Non-existence, instability, and growth theorems for solutions of a class of abstract nonlinear equations with applications to nonlinear elastodynamics
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Essentially nonlinear one-dimensional model of classical field theory
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Blow-up theorems for nonlinear wave equations
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Development of Singularities of Solutions of Nonlinear Hyperbolic Partial Differential Equations
inferredcites →https://doi.org/10.1063/1.1724290openalex-snapshot
Exact Solution for the Vibrations of a Nonlinear Continuous Model String
inferredcites →https://doi.org/10.1090/mmono/023openalex-snapshot
Linear and Quasi-linear Equations of Parabolic Type
inferredcites →https://doi.org/10.1090/pspum/018.1/0269995openalex-snapshot
On some nonexistence and nonuniqueness theorems for nonlinear parabolic equations
inferredcites →https://doi.org/10.1090/s0002-9939-1975-0365265-9openalex-snapshot
Further Global Nonexistence Theorems for Abstract Nonlinear Wave Equations
inferredcites →https://doi.org/10.1090/s0002-9947-1974-0344697-2openalex-snapshot
Instability and nonexistence of global solutions to nonlinear wave equations of the form 𝑃𝑢_{𝑡𝑡}=-𝐴𝑢+ℱ(𝓊)
inferredcites →https://doi.org/10.1103/physrevlett.30.1262openalex-snapshot
Method for Solving the Sine-Gordon Equation
inferredcites →https://doi.org/10.1143/ptp.51.703openalex-snapshot
On the Toda Lattice. II: Inverse-Scattering Solution

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Unique continuation for the Benjamin-Bona-Mahony and Boussinesq's equations
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Exponential growth of positive initial-energy solutions of a system of nonlinear viscoelastic wave equations with damping and source terms
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Optimal decay rate and blow-up of solution for a classical thermoelastic system with viscoelastic damping and nonlinear sources
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Refined Long Time Existence of the Boussinesq Equation with Large Initial Data in $$\mathbb {R}^{n}$$
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Blow up of Solutions of a Nonlinear Viscoelastic Wave Equation
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Well-posedness of 2-D hyperbolic viscous Cahn-Hilliard equation
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Solution blowup for the heat equation with double nonlinearity
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Periodic boundary value problem and cauchy problem of the generalized cubic double dispersion equation
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Finite time blow up of the solutions to boussinesq equation with linear restoring force and arbitrary positive energy
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Blow-up of solution of an initial boundary value problem for a damped nonlinear hyperbolic equation
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Blow-up of solutions to quasilinear parabolic equations
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Nonexistence of global solutions of a hyperbolic problem
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Global existence for the generalised 2D Ginzburg-Landau equation
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Cauchy problem for a damped generalized IMBq equation
inferred← citeshttps://doi.org/10.1063/1.4798786openalex-snapshot
Global solvability and blow up for the convective Cahn-Hilliard equations with concave potentials
inferred← citeshttps://doi.org/10.1063/1.4934319openalex-snapshot
Generalized Nehari functionals and finite time blow up of the solutions to Boussinesq equation
inferred← citeshttps://doi.org/10.1063/5.0004276openalex-snapshot
A class of nonlinear parabolic equations with anisotropic nonstandard growth conditions
inferred← citeshttps://doi.org/10.1063/5.0089480openalex-snapshot
The Kirchhoff-type diffusion problem driven by a magnetic fractional Laplace operator
inferred← citeshttps://doi.org/10.1063/5.0149240openalex-snapshot
Qualitative properties of solution to a viscoelastic Kirchhoff-like plate equation
inferred← citeshttps://doi.org/10.1063/5.0177675openalex-snapshot
Finite time blow up of solutions to Klein-Gordon equation with variable coefficients nonlinearities
inferred← citeshttps://doi.org/10.1070/im2011v075n04abeh002550openalex-snapshot
On the blow-up of internal gravitational waves with non-linear sources
inferred← citeshttps://doi.org/10.1070/im2012v076n02abeh002584openalex-snapshot
Blow-up of ion-sound waves in plasma with non-linear sources on the boundary
inferred← citeshttps://doi.org/10.1070/im2012v076n03abeh002596openalex-snapshot
Blow-up of solutions of an inhomogeneous system of Sobolev-type equations
inferred← citeshttps://doi.org/10.1070/im2013v077n02abeh002638openalex-snapshot
Blow-up of solutions of strongly dissipative generalized Klein-Gordon equations
inferred← citeshttps://doi.org/10.1070/im2014v078n03abeh002696openalex-snapshot
Blow-up of solutions of non-linear equations of Kadomtsev-Petviashvili and Zakharov-Kuznetsov types
inferred← citeshttps://doi.org/10.1070/im2014v078n05abeh002714openalex-snapshot
Blow-up of solutions of an abstract Cauchy problem for a formally hyperbolic equation with double non-linearity
inferred← citeshttps://doi.org/10.1070/im8579openalex-snapshot
Blow-up of solutions of a full non-linear equation of ion-sound waves in a plasma with non-coercive non-linearities
inferred← citeshttps://doi.org/10.1070/im8880openalex-snapshot
Blow-up and global solubility in the classical sense of the Cauchy problem for a formally hyperbolic equation with a non-coercive source
inferred← citeshttps://doi.org/10.1070/sm2009v200n04abeh004008openalex-snapshot
Blow-up of Oskolkov's system of equations
inferred← citeshttps://doi.org/10.1070/sm2011v202n01abeh004137openalex-snapshot
Blow-up of ion acoustic waves in a plasma
inferred← citeshttps://doi.org/10.1070/sm2013v204n03abeh004303openalex-snapshot
Solution blow-up for a class of parabolic equations with double nonlinearity
inferred← citeshttps://doi.org/10.1080/00036810108840993openalex-snapshot
Golbal nonexistence in a nonlinearly damped wave equation
inferred← citeshttps://doi.org/10.1080/00036810310001620045openalex-snapshot
Global Existence and Decay for Solutions to the “Bad” Boussinesq Equation in Two Space Dimensions
inferred← citeshttps://doi.org/10.1080/00036811.2010.549475openalex-snapshot
Global existence and decay of solutions of a nonlinear system of wave equations
inferred← citeshttps://doi.org/10.1080/00036811.2014.956733openalex-snapshot
Blow-up in a semilinear parabolic problem with variable source under positive initial energy
inferred← citeshttps://doi.org/10.1080/00036811.2015.1038994openalex-snapshot
Sign-preserving functionals and blow-up to Klein–Gordon equation with arbitrary high energy
inferred← citeshttps://doi.org/10.1080/00036811.2017.1313410openalex-snapshot
A note on blow-up of solutions for a class of fourth-order wave equation with viscous damping term
inferred← citeshttps://doi.org/10.1080/00036811.2021.1947494openalex-snapshot
Blow-up phenomenon for a semilinear pseudo-parabolic equation involving variable source
inferred← citeshttps://doi.org/10.1080/00036811.2022.2078716openalex-snapshot
Lower and upper bounds for the blow-up time to a viscoelastic Petrovsky wave equation with variable sources and memory term
inferred← citeshttps://doi.org/10.1080/00036811.2025.2450692openalex-snapshot
Stability and instability for a viscoelastic Kirchhoff heat equation with variable sources
inferred← citeshttps://doi.org/10.1080/00036819008839928openalex-snapshot
On the Blow-up of Certain Solutions of the “Good” Boussinesq Equation
inferred← citeshttps://doi.org/10.1080/01495739.2026.2669231openalex-snapshot
Analytical and finite element study of thermally-induced blow-up in nonlinear delayed wave systems for viscoelastic beams
inferred← citeshttps://doi.org/10.1080/03605302.2010.484472openalex-snapshot
On Global Attractor for 2D Kirchhoff-Boussinesq Model with Supercritical Nonlinearity
inferred← citeshttps://doi.org/10.1080/03605308508820396openalex-snapshot
An existence theory for water waves and the boussinesq and korteweg-devries scaling limits
inferred← citeshttps://doi.org/10.1080/03605308908820597openalex-snapshot
Some global dynamical properties of a class of pattern formation equations
inferred← citeshttps://doi.org/10.1080/03605309608821225openalex-snapshot
Existance and Uniqueness for Boussinesq type equations on a circle
inferred← citeshttps://doi.org/10.1088/0266-5611/23/1/015openalex-snapshot
Wronskian solutions of the Boussinesq equation—solitons, negatons, positons and complexitons
inferred← citeshttps://doi.org/10.1088/0266-5611/24/3/035012openalex-snapshot
The Boussinesq equation with self-consistent sources
inferred← citeshttps://doi.org/10.1088/0951-7715/23/1/006openalex-snapshot
Global existence and blow-up for a class of nonlocal nonlinear Cauchy problems arising in elasticity
inferred← citeshttps://doi.org/10.1090/s0025-5718-09-02231-5openalex-snapshot
Approximation of nonlinear wave equations with nonstandard anisotropic growth conditions
inferred← citeshttps://doi.org/10.1103/physreve.47.r13openalex-snapshot
Nonstable solitons and sharp criteria for wave collapse
inferred← citeshttps://doi.org/10.1103/physreve.47.r796openalex-snapshot
Blow-up in the Boussinesq equation
inferred← citeshttps://doi.org/10.1109/icmt.2011.6002406openalex-snapshot
The existence and nonexistence of global solutions for a nonlinear hyperbolic equation
inferred← citeshttps://doi.org/10.1111/sapm.70195openalex-snapshot
On a Class of Viscoelastic Plate Equations Modeling the Oscillations of Suspension Bridges
inferred← citeshttps://doi.org/10.11131/2017/101258openalex-snapshot
Exponential Growth of Solution for a Class of Reaction Diffusion Equation with Memory and Multiple Nonlinearities
inferred← citeshttps://doi.org/10.1134/s0001434612010233openalex-snapshot
Blow-up of the solution of an inhomogeneous system of Sobolev-type equations
inferred← citeshttps://doi.org/10.1134/s0001434614030274openalex-snapshot
Blow-up in systems with nonlinear viscosity
inferred← citeshttps://doi.org/10.1134/s0001434615050247openalex-snapshot
On local solvability and blow-up of solutions of an abstract nonlinear Volterra integral equation
inferred← citeshttps://doi.org/10.1134/s0001434622090097openalex-snapshot
Blow-Up of Solutions of Coupled Parabolic Systems and Hyperbolic Equations
inferred← citeshttps://doi.org/10.1134/s0012266122050056openalex-snapshot
Operator Equations of the Second Kind: Theorems on the Existence and Uniqueness of the Solution and on the Preservation of Solvability
inferred← citeshttps://doi.org/10.1134/s0016266324030092openalex-snapshot
Inverse Problem for the $$L$$-Operator in the Lax Pair of the Boussinesq Equation on the Circle
inferred← citeshttps://doi.org/10.1134/s0037446611030098openalex-snapshot
On blowup of solutions to a system of equations of ion sound waves in plasma
inferred← citeshttps://doi.org/10.1134/s003744661204012xopenalex-snapshot
On blowup of solutions to a Kirchhoff type dissipative wave equation with a source and positive energy
inferred← citeshttps://doi.org/10.1134/s0040577917110010openalex-snapshot
Local solvability and solution blow-up of one-dimensional equations of the Yajima–Oikawa–Satsuma type
inferred← citeshttps://doi.org/10.1134/s0040577921030065openalex-snapshot
Soliton-like excitations in weakly dispersive media
inferred← citeshttps://doi.org/10.1134/s0965542510050088openalex-snapshot
Solution blow-up for a new stationary Sobolev-type equation
inferred← citeshttps://doi.org/10.1134/s0965542511030080openalex-snapshot
Finite-time relaxation of the solution of a nonlinear pseudoparabolic equation
inferred← citeshttps://doi.org/10.1134/s0965542515110056openalex-snapshot
Numerical study of solitary waves and reversible shock structures in tubes with controlled pressure
inferred← citeshttps://doi.org/10.1134/s0965542516100122openalex-snapshot
Blowup of the solution to the Cauchy problem with arbitrary positive energy for a system of Klein–Gordon equations in the de Sitter metric
inferred← citeshttps://doi.org/10.1134/s0965542518030077openalex-snapshot
Solution Blow-up in a Nonlinear System of Equations with Positive Energy in Field Theory
inferred← citeshttps://doi.org/10.1134/s0965542519040067openalex-snapshot
Blow-up of Solutions of Nonclassical Nonlocal Nonlinear Model Equations
inferred← citeshttps://doi.org/10.1134/s1995080220090061openalex-snapshot
Solvability of Pseudoparabolic Equations with Non-Linear Boundary Condition
inferred← citeshttps://doi.org/10.1134/s1995080224605678openalex-snapshot
Blow-up Phenomena for a Pseudo-parabolic Equation on Stratified Groups
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