Polynomial decay rate for a new class of viscoelastic Kirchhoff equation related with Balakrishnan-Taylor dissipation and logarithmic source terms

Qualitative analysis of solutions for the p‐Laplacian hyperbolic equation with logarithmic nonlinearity

“…The logarithmic nonlinearity arises in a lot of different areas of physics such as quantum mechanics, nuclear physics, inflation cosmology, and supersymmetric field theories 1‐3,13 . This type of nonlinearity was introduced in the nonrelativistic wave equations describing spinning particles moving in an external electromagnetic field and also in the relativistic wave equation for spinless particles 4,30,31 . Moreover, the logarithmic nonlinearity appears in several branches of physics such as inflationary cosmology, 5 nuclear physics, 6 optics, 7 and geophysics 8 .…”

“…[1][2][3]13 This type of nonlinearity was introduced in the nonrelativistic wave equations describing spinning particles moving in an external electromagnetic field and also in the relativistic wave equation for spinless particles. 4,30,31 Moreover, the logarithmic nonlinearity appears in several branches of physics such as inflationary cosmology, 5 nuclear physics, 6 optics, 7 and geophysics. 8 With all those specific underlying meaning in physics, the global-in-time well-posedness of solution to the problem of evolution equation with such logarithmic type nonlinearity captures lots of attention.…”

Multiplicity Solutions of Fractional Impulsive p -Laplacian Systems: New Result

“…In viscoelasticity, electrochemistry, power, porous media, and electromagnetism, for instance, see and the references therein. Many articles have recently investigated the existence of solutions to boundary value problems for FDEs, and we refer the reader to one of them [2,[18][19][20][34][35][36][37][38][39][40][41][42][43][44][45][46] and the references therein. For example, Kamache et al [40] investigated the existence of three solutions for a class of fractional p-Laplacian systems using a variational structure and critical point theory.…”

General decay of nonlinear viscoelastic Kirchhoff equation with Balakrishnan‐Taylor damping, logarithmic nonlinearity and distributed delay terms

“…Viscoelasticity is included in the study of biological materials. A viscoelastic material will return to its original shape after any deforming force has been removed even though it will take time to do so (see previous studies) 1‐12 …”

“…Either in the presence of the Balakrishnan‐Taylor damping term ( σ ≠ 0), which was proposed by Balakrishnan and Taylor, 13 since then, many works have been studied and there are many results regarding existence and asymptotic behavior (see previous works 8,14 ). Also, our problem with ( σ ≠ 0 and ) was studied by Boulaaras 4,14 and who established the stability result under certain conditions on the kernel g .…”