The regularity properties and blow-up of solutions for nonlocal wave equations and applications
DOI10.1007/s00025-022-01752-yzbMath1500.35078OpenAlexW4303926803MaRDI QIDQ2081548
Veli B. Shakhmurov, Rishad Shahmurov
Publication date: 13 October 2022
Published in: Results in Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00025-022-01752-y
Fourier multiplierswave equationsregularity propertiesabstract differential equationsblow-up of solutions
Smoothness and regularity of solutions to PDEs (35B65) Initial-boundary value problems for second-order hyperbolic equations (35L20) Spaces of vector- and operator-valued functions (46E40) Linear symmetric and selfadjoint operators (unbounded) (47B25) Abstract hyperbolic equations (35L90) Blow-up in context of PDEs (35B44)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Linear and nonlinear degenerate abstract differential equations with small parameter
- Optimal decay estimates for the general solution to a class of semi-linear dissipative hyperbolic equations
- Embeddings and separable differential operators in spaces of Sobolev-lions type
- Formulations of nonlocal continuum mechanics based on a new definition of stress tensor
- Almost global wellposedness of the 2-D full water wave problem
- Semigroups of linear operators and applications to partial differential equations
- Global existence of smooth solutions and stability of solitary waves for a generalized Boussinesq equation
- Global existence of small solutions for a generalized Boussinesq equation
- The initial value problem for a generalized Boussinesq equation.
- Small amplitude solutions of the generalized IMBq equation.
- Reformulation of elasticity theory for discontinuities and long-range forces
- Nonlinear stability of rarefaction waves for the Boltzmann equation
- Cauchy problem of the generalized double dispersion equation
- Nonlocal Continuum Field Theories
- Solitary-Wave Interactions in Elastic Rods
- Commutator estimates and the euler and navier-stokes equations
- Periodic solutions of a nonlinear wave equation
- Blow up of solutions of a generalized Boussinesq equation
- Existence and nonexistence of global solutions for the generalized IMBq equation
- Instability and Nonexistence of Global Solutions to Nonlinear Wave Equations of the Form Pu tt = -Au + ℱ(u)
- Operator–valued Fourier multiplier theorems on Besov spaces
- Instability and Blow-Up of Solutions to a Generalized Boussinesq Equation
- Derivation of Higher Order Gradient Continuum Models from Atomistic Models for Crystalline Solids
- Global existence and blow-up for a class of nonlocal nonlinear Cauchy problems arising in elasticity
- Nonlocal elasticity and related variational principles
This page was built for publication: The regularity properties and blow-up of solutions for nonlocal wave equations and applications