Exponential integrators with adaptive meshing for nonlocal blow-up dynamics

The blow-up dynamic and upper bound on the blow-up rate for critical nonlinear Schrödinger equation

10.4007/annals.2005.161.157 · doi-reference

Convergent finite difference schemes for nonlinear parabolic equations

10.1137/0709048 · doi-reference

Semi-Lagrangian adaptive mesh method for singularly perturbed differential equation with interior turning point

10.1016/j.cnsns.2026.109896 · doi-reference

Positivity-preserving and energy-dissipative finite difference schemes for the Fokker–Planck and Keller–Segel equations

10.1093/imanum/drac014 · doi-reference

A conservative and positivity-preserving discontinuous Galerkin method for the population balance equation

10.1007/s10915-026-03197-9 · doi-reference

Improved uniform error bounds on a Lawson-type exponential integrator for the long-time dynamics of sine-Gordon equation

10.1007/s00211-024-01423-w · doi-reference

Exponential integrators

10.1017/s0962492910000048 · doi-reference

Semiglobal oblique projection exponential dynamical observers for nonautonomous semilinear parabolic-like equations

10.1007/s00332-021-09756-8 · doi-reference

Analysis of a new time-space two-grid method for the two-dimensional nonlinear nonlocal mobile/immobile transport model

10.1007/s10915-026-03314-8 · doi-reference

A new high-order compact CN-ADI scheme on graded meshes for three-dimensional nonlinear PIDEs with multiple weakly singular kernels

10.1016/j.aml.2025.109697 · doi-reference

Blow-up rate estimate for degenerate parabolic equation with nonlinear gradient term

10.1007/s10483-010-1313-6 · doi-reference

Gradient blowup behavior for a viscous Hamilton-Jacobi equation with degenerate gradient nonlinearity

10.1016/j.jde.2023.02.030 · doi-reference

Classification of blowup solutions for a parabolic p-laplacian equation with nonlinear gradient terms

10.1016/j.jmaa.2015.12.044 · doi-reference

Sign-changing solution for an elliptic equation with critical growth at the boundary

10.1007/s00030-024-00990-z · doi-reference

Asymptotic expansions for singular solutions of δu+eu=0 in a punctured disc

10.1007/s00526-021-01926-6 · doi-reference

Blowup time estimates for a parabolic p-laplacian equation with nonlinear gradient terms

10.1007/s00033-019-1133-z · doi-reference

Finite-time singularity formation for strong solutions to the Boussinesq system

10.1007/s40818-020-00080-0 · doi-reference

Local behaviour of the solutions of the Chipot-Weissler equation

10.1007/s00526-023-02580-w · doi-reference

A priori estimates for elliptic equations with reaction terms involving the function and its gradient

10.1007/s00208-019-01872-x · doi-reference

A priori estimates of solutions to local and nonlocal superlinear parabolic problems

10.1007/s00028-025-01095-5 · doi-reference

Nonexistence of positive solutions for nonlinear parabolic robin problems and hardy-leray inequalities

10.1007/s10231-022-01226-6 · doi-reference

Critical exponents for the p-Laplace heat equations with combined nonlinearities

10.1007/s00028-023-00922-x · doi-reference

A priori estimates and Liouville-type theorems for the semilinear parabolic equations involving the nonlinear gradient source

10.1007/s00526-024-02907-1 · doi-reference

Existence of a stable blow-up profile for the nonlinear heat equation with a critical power nonlinear gradient term

10.1090/tran/7631 · doi-reference

Blow-up for semilinear parabolic equations with nonlinear memory

10.1007/s00033-003-1128-6 · doi-reference

Blow-up of solutions of parabolic equations with nonlinear memory

10.1016/0022-0396(87)90168-9 · doi-reference

Boundedness versus blow-up in a chemotaxis system

10.1016/j.jde.2004.10.022 · doi-reference

Some blowup results for a nonlinear parabolic equation with a gradient term

10.1137/0520060 · doi-reference